,((($&0 75$16$&7,216 21 1(7:25.,1* 92/ 12 )(%58$5< &RQQHFWLYLW\%DVHG 6HJPHQWDWLRQ LQ /DUJH6FDOH
'' 6HQVRU 1HWZRUNV $OJRULWKP
DQG $SSOLFDWLRQV
+RQJER -LDQJ, Member, IEEE 7LDQORQJ <X, Student Member, IEEE &KHQ 7LDQ, Member, IEEE
*XDQJ 7DQ , Member, IEEE, ACM DQG &KRQJJDQJ :DQJ, Senior Member, IEEE
Abstract—(I¿FLHQW VHQVRU QHWZRUN GHVLJQ UHTXLUHV D IXOO
XQGHUVWDQGLQJ RI WKH JHRPHWULF HQYLURQPHQW LQ ZKLFK VHQVRU
QRGHV DUH GHSOR\HG ,Q SUDFWLFH D ODUJHVFDOH VHQVRU QHWZRUN
RIWHQ KDV D FRPSOH[ DQG LUUHJXODU WRSRORJ\ SRVVLEO\ FRQWDLQLQJ
REVWDFOHVKROHV &RQYH[ QHWZRUN SDUWLWLRQLQJ DOVR NQRZQ DV
convex segmentation LV D WHFKQLTXH WR GLYLGH D QHWZRUN LQWR
FRQYH[ UHJLRQV LQ ZKLFK WUDGLWLRQDO DOJRULWKPV GHVLJQHG IRU D
VLPSOH QHWZRUN JHRPHWU\ FDQ EH DSSOLHG ([LVWLQJ VHJPHQWDWLRQ
DOJRULWKPV KHDYLO\ GHSHQG RQ FRQFDYH QRGH GHWHFWLRQ RU VLQN
H[WUDFWLRQ IURP WKH PHGLDQ D[LVVNHOHWRQ UHVXOWLQJ LQ VHQVLWLYLW\ RI
SHUIRUPDQFH WR QHWZRUN ERXQGDU\ QRLVH )XUWKHUPRUH VLQFH WKH\
UHO\ RQ WKH QHWZRUN
V ' JHRPHWULF SURSHUWLHV WKH\ GR QRW ZRUN
IRU ' FDVHV 7KLV SDSHU SUHVHQWV D QRYHO VHJPHQWDWLRQ DSSURDFK
EDVHG RQ Morse function EULQJLQJ WRJHWKHU WKH QRWLRQV RI FRQYH[
FRPSRQHQWV DQG WKH Reeb graph RI D QHWZRUN 7KH VHJPHQWDWLRQ LV
UHDOL]HG E\ D GLVWULEXWHG DQG VFDODEOH DOJRULWKP QDPHG CONSEL
IRU &21QHFWLYLW\EDVHG 6(JPHQWDWLRQ LQ /DUJHVFDOH ''
VHQVRU QHWZRUNV ,Q &216(/ VHYHUDO ERXQGDU\ QRGHV ¿UVW ÀRRG
WKH QHWZRUN WR FRQVWUXFW WKH 5HHE JUDSK 7KH RUGLQDU\ QRGHV WKHQ
FRPSXWH PXWH[ SDLUV ORFDOO\ JHQHUDWLQJ D FRDUVH VHJPHQWDWLRQ
1H[W QHLJKERULQJ UHJLRQV WKDW DUH QRW PXWH[ SDLUV DUH PHUJHG
WRJHWKHU )LQDOO\ E\ LJQRULQJ PXWH[ SDLUV WKDW OHDG WR VPDOO
0DQXVFULSW UHFHLYHG 'HFHPEHU UHYLVHG 'HFHPEHU DQG
2FWREHU DFFHSWHG 1RYHPEHU DSSURYHG E\ ,((($&0
75$16$&7,216 21 1(7:25.,1* ' 0DQMXQDWK 'DWH RI SXEOLFDWLRQ 1RYHPEHU
GDWH RI FXUUHQW YHUVLRQ )HEUXDU\ 7KLV ZRUN ZDV VXSSRUWHG
LQ SDUW E\ WKH 1DWLRQDO 1DWXUDO 6FLHQFH )RXQGDWLRQ RI &KLQD XQGHU *UDQWV
DQG WKH 1DWLRQDO 1DWXUDO 6FLHQFH
)RXQGDWLRQ RI &KLQD DQG 0LFURVRIW 5HVHDUFK $VLD XQGHU *UDQW WKH )XQGDPHQWDO 5HVHDUFK )XQGV IRU WKH &HQWUDO 8QLYHUVLWLHV XQGHU *UDQW
41 WKH 1DWLRQDO 1DWXUDO 6FLHQFH )RXQGDWLRQ RI +XEHL 3URYLQFH
XQGHU *UDQW &'% WKH &+87,$1 6FKRODU 3URMHFW RI +XEHL 3URYLQFH
WKH <RXWK &KHQJXDQJ 3URMHFW RI :XKDQ &LW\ XQGHU *UDQW WKH
6FLHQWL¿F 5HVHDUFK )RXQGDWLRQ IRU WKH 5HWXUQHG 2YHUVHDV &KLQHVH 6FKRODUV
6WDWH (GXFDWLRQ 0LQLVWU\ DQG WKH 3URJUDP IRU 1HZ &HQWXU\ ([FHOOHQW 7DOHQWV
LQ 8QLYHUVLW\ XQGHU *UDQW 1&(7 6WDWH (GXFDWLRQ 0LQLVWU\ 7KH ZRUN
RI * 7DQ ZDV VXSSRUWHG E\ WKH 1DWLRQDO 1DWXUDO 6FLHQFH )RXQGDWLRQ RI &KLQD
XQGHU *UDQW WKH <RXWK ,QQRYDWLRQ 3URPRWLRQ $VVRFLDWLRQ WKH
&KLQHVH $FDGHP\ RI 6FLHQFHV WKH 0LQLVWU\ RI 6FLHQFH DQG 7HFKQRORJ\ XQGHU
.H\ 3URMHFW 1R $$ DQG WKH 6KHQ]KHQ 2YHUVHDV +LJKOHYHO
7DOHQWV ,QQRYDWLRQ DQG (QWUHSUHQHXUVKLS )XQGV XQGHU .4&$
$Q HDUO\ YHUVLRQ RI WKLV ZRUN DSSHDUHG LQ WKH 3URFHHGLQJV RI WKH ,((( ,QWHUQD
WLRQDO &RQIHUHQFH RQ &RPSXWHU &RPPXQLFDWLRQV ,1)2&20 2UODQGR )/
86$ 0DUFK ± + -LDQJ 7 <X DQG & 7LDQ DUH ZLWK WKH 'HSDUWPHQW RI (OHFWURQLFV DQG
,QIRUPDWLRQ (QJLQHHULQJ :XKDQ 1DWLRQDO /DERUDWRU\ IRU 2SWRHOHFWURQLFV
+XD]KRQJ 8QLYHUVLW\ RI 6FLHQFH DQG 7HFKQRORJ\ :XKDQ &KLQD
HPDLO KRQJERMLDQJ#JPDLOFRP
* 7DQ LV ZLWK 6,$7 &KLQHVH $FDGHP\ RI 6FLHQFHV 6KHQ]KHQ &KLQD
& :DQJ LV ZLWK ,QWHU'LJLWDO &RPPXQLFDWLRQV .LQJ RI 3UXVVLD 3$ 86$
&RORU YHUVLRQV RI RQH RU PRUH RI WKH ¿JXUHV LQ WKLV SDSHU DUH DYDLODEOH RQOLQH
DW KWWSLHHH[SORUHLHHHRUJ
'LJLWDO 2EMHFW ,GHQWL¿HU 71(7
)LJ 7KH WRSRORJLHV RI DQ 6VKDSHG FRDO PLQH WXQQHO DQG WKH &KLFDJR DLUSRUW
WHUPLQDO EXLOGLQJ
FRQFDYLW\ ZH SURYLGH DQ DSSUR[LPDWH FRQYH[ GHFRPSRVLWLRQ
&216(/ KDV D QXPEHU RI DGYDQWDJHV RYHU SUHYLRXV VROXWLRQV
LW ZRUNV IRU ERWK ' DQG ' VHQVRU QHWZRUNV LW XVHV PHUHO\
QHWZRUN FRQQHFWLYLW\ LQIRUPDWLRQ LW JXDUDQWHHV D ERXQG IRU WKH
JHQHUDWHG UHJLRQV
GHYLDWLRQ IURP FRQYH[LW\ :H IXUWKHU SURSRVH
WR LQWHJUDWH QHWZRUN VHJPHQWDWLRQ ZLWK H[LVWLQJ DSSOLFDWLRQV WKDW
DUH RULHQWHG WR VLPSOH QHWZRUN JHRPHWU\ ([WHQVLYH VLPXODWLRQV
VKRZ WKH HI¿FDF\ RI &216(/ LQ VHJPHQWLQJ QHWZRUNV DQG LQ LP
SURYLQJ WKH SHUIRUPDQFH RI WZR DSSOLFDWLRQV JHRJUDSKLF URXWLQJ
DQG FRQQHFWLYLW\EDVHG ORFDOL]DWLRQ
Index Terms—/RFDOL]DWLRQ URXWLQJ VHJPHQWDWLRQ ZLUHOHVV
VHQVRU QHWZRUNV
5
, ,1752'8&7,21
(&(17 \HDUV KDYH ZLWQHVVHG D ZLGH XVDJH RI ' ZLUH
OHVV VHQVRU QHWZRUNV :61V LQ HPHUJLQJ DSSOLFDWLRQV
ZKHUH QRGHV DUH W\SLFDOO\ GHSOR\HG LQ ' VHWWLQJV VXFK DV
VDIHW\ PRQLWRULQJ RI FRDO PLQH WXQQHOV >@ >)LJ D@ DQG ¿UH
GHWHFWLRQ LQ WKH FRUULGRUV RI EXLOGLQJV >@ >)LJ E@ (I¿
FLHQW VHQVRU QHWZRUN GHVLJQ UHTXLUHV D IXOO XQGHUVWDQGLQJ RI WKH
JHRPHWULF HQYLURQPHQW LQ ZKLFK VHQVRU QRGHV DUH GHSOR\HG ,Q
SUDFWLFH WKH JOREDO WRSRORJ\ RI D ODUJHVFDOH VHQVRU QHWZRUN
LV UDUHO\ LQ D VLPSOH RU UHJXODU VKDSH VXFK DV D VTXDUH RU D
GLVN DV DVVXPHG LQ PDQ\ SUHYLRXV VWXGLHV HJ >@ DQG >@
)RU H[DPSOH JHRJUDSKLF URXWLQJ >@ LV D URXWLQJ VFKHPH IRU
VHQVRU QHWZRUNV ZKHUH D QRGH PDNHV URXWLQJ GHFLVLRQV JUHHGLO\
EDVHG RQ D ORFDO FRRUGLQDWHV 6SHFL¿FDOO\ D QRGH URXWHV D PHV
VDJH WR LWV QHLJKERU FORVHVW WR WKH GHVWLQDWLRQ 'HVSLWH LWV VXF
FHVV LQ UHJXODU VHQVRU ¿HOGV WKLV SURWRFRO IDLOV RU SHUIRUPV
SRRUO\ LQ LUUHJXODU DQG FRQFDYH DUHDV >@ >@ >@ >@
>@ $OVR LUUHJXODU QHWZRUN VKDSHV PD\ OHDG WR LQDFFXUDWH OR
FDOL]DWLRQ UHVXOWV DV PDQ\ H[LVWLQJ ORFDOL]DWLRQ DOJRULWKPV DV
VXPH VWUDLJKWOLQH VKRUWHVW SDWKV EHWZHHQ QRGHV 7KLV GRHV QRW
,((( 3HUVRQDO XVH LV SHUPLWWHG EXW UHSXEOLFDWLRQUHGLVWULEXWLRQ UHTXLUHV ,((( SHUPLVVLRQ
6HH KWWSZZZLHHHRUJSXEOLFDWLRQVBVWDQGDUGVSXEOLFDWLRQVULJKWVLQGH[KWPO IRU PRUH LQIRUPDWLRQ
,((($&0 75$16$&7,216 21 1(7:25.,1* 92/ 12 )(%58$5< )LJ 1HWZRUN RI QRGHV 7KH DYHUDJH QRGH GHJUHH LV D 6NHOHWRQ UHVXOW E\ >@ ZKHUH QRGHV LQ VNHOHWRQ DUH VKRZQ LQ GDUN JUHHQ E 6HJPHQWDWLRQ
UHVXOW E\ >@ RU >@ ZKHUH QR REYLRXV JHRPHWULF IHDWXUHV RQ WKH ERXQGDU\ H[LVW ([LVWLQJ DOJRULWKPV JHQHUDWH D VLQJOH UHJLRQ F 6HJPHQWDWLRQ UHVXOW E\ &216(/
ZKHUH IRXU DSSUR[LPDWHO\ FRQYH[ UHJLRQV DUH JHQHUDWHG
KROG ZKHQ WKH QHWZRUN WRSRORJ\ LV KLJKO\ LUUHJXODU UHVXOWLQJ LQ
GLVWRUWHG SDWK OHQJWK HVWLPDWLRQ >@ >@ DQG WKXV LQDFFXUDWH
ORFDOL]DWLRQ UHVXOWV
1XPHURXV PHWKRGV >@±>@ KDYH EHHQ SURSRVHG WR LPSURYH
WKH WUDGLWLRQDO DOJRULWKPV
SHUIRUPDQFH E\ DGDSWLQJ WKHP WR LU
UHJXODU VHQVRU ¿HOG 7KHVH HIIRUWV DUH PRVWO\ DSSOLFDWLRQVSH
FL¿F LQFUHDVLQJ WKH GHVLJQ FRPSOH[LW\ VLJQL¿FDQWO\ $OWHUQD
WLYHO\ WR WDPH WKH FKDOOHQJHV EURXJKW E\ LUUHJXODU VKDSHV WKHUH
KDV EHHQ DQ LQFUHDVLQJ LQWHUHVW RQ D FRQYH[ QHWZRUN SDUWLWLRQ
DOVR NQRZQ DV segmentationconvex partition >@ >@ LQ WKLV
SDSHU ZH FRQVLGHU VKDSH VHJPHQWDWLRQ LQVWHDG RI GDWD VHJPHQ
WDWLRQ >@ RU VLJQDO ¿HOG VHJPHQWDWLRQ >@ ZKLFK LV WR GLYLGH
D QHWZRUN LQWR FRQYH[ UHJLRQV RU VXEQHWZRUNV VR WKDW WUDGL
WLRQDO DOJRULWKPV GHVLJQHG IRU D VLPSOH JHRPHWULF UHJLRQ FDQ EH
DSSOLHG ZLWK JRRG SHUIRUPDQFH %\ GRLQJ VR ZLWKRXW KHDYLO\
PRGLI\LQJ SDUWLFXODU DOJRULWKPV WUDGLWLRQDO DOJRULWKPV DUH DEOH
WR SHUIRUP ZHOO LQ HDFK FRQYH[ UHJLRQ
A. Related Work
$ SLRQHHU SLHFH RI ZRUN RQ VHQVRU QHWZRUN VHJPHQWDWLRQ LV
>@ ,W ¿UVW H[WUDFWV WKH VNHOHWRQ DQG FRQVWUXFWV WKH GLVWDQFH ¿HOG
RI D QHWZRUN 1H[W EDVHG RQ ÀRZ FRPSOH[ >@ D QRGH RQ D ÀRZ
LV DVVLJQHG D ÀRZ GLUHFWLRQ DQG LGHQWL¿HV LWVHOI DV D VLQN LI WKHUH
LV QR ÀRZ GLUHFWLRQ $FFRUGLQJ WR WKH ÀRZ GLUHFWLRQ WR WKH VLQN
WKH RUGLQDU\ QRGHV DUH JURXSHG LQWR UHJLRQV ,QVSLUHG E\ SRO\J
RQDO SDUWLWLRQ WKH VROXWLRQ LQ >@ SDUWLWLRQV WKH QHWZRUN YLD FRQ
FDYH QRGH LGHQWL¿FDWLRQ RQ WKH ERXQGDU\ 7KH PDLQ LGHD RI WKHLU
DOJRULWKP LV WR SHUIRUP ELVHFWRULQGXFHG FRQYH[ SDUWLWLRQLQJ
7KHVH VHJPHQWDWLRQ DOJRULWKPV XQIRUWXQDWHO\ GHSHQG RQ WKH
H[LVWHQFH RI QRGHV RQ GLVWLQJXLVKHG FRQFDYH ERXQGDULHV DQG
WKXV WKH\ PD\ IDLO IRU QHWZRUNV ZKHUH QR VXFK QRGHV RU VLQNV
RQ WKH VNHOHWRQ H[LVW DV VKRZQ LQ )LJ 7KH UHDVRQ LV WKDW WKHLU
DOJRULWKPV GR QRW FRQVLGHU WKH JOREDO WRSRORJ\ RI WKH QHWZRUN
%HVLGHV WKLV GHSHQGHQF\ PDNHV WKHLU SHUIRUPDQFH TXLWH VHQVL
WLYH WR ERXQGDU\ QRLVH HJ LQFRUUHFW HVWLPDWLRQ RI ERXQGDULHV
/DVWO\ VLQFH WKH\ UHO\ RQ WKH QHWZRUN
V ' JHRPHWULF SURSHU
WLHV WKH\ FDQQRW ZRUN IRU ' VHQVRU QHWZRUNV ,Q D ' VSDFH
ZH DUH DZDUH RI RQH SDUWLDO VROXWLRQ SURSRVHG LQ >@ EDVHG RQ
ERWWOHQHFN LGHQWL¿FDWLRQ $ SDUDPHWHU QDPHG injectivity radius
LV FDOFXODWHG E\ HDFK ERXQGDU\ QRGH 7KH SXUSRVH RI WKLV SDUDP
HWHU LV WR PHDVXUH WKH QDUURZQHVV RI WKH QHDUE\ ERXQGDU\ DUHD
VR DV WR LGHQWLI\ WKH XQGHVLUHG ERWWOHQHFNV LQ D ' VHQVRU QHW
ZRUN 7KHVH ERWWOHQHFNV DUH WKHQ XVHG WR SDUWLWLRQ WKH QHWZRUN
ERXQGDU\ DQG WKH QRQERXQGDU\ QRGHV DUH JURXSHG ¿QDOO\ 7KXV
WKLV DOJRULWKP GRHV QRW ZRUN IRU QHWZRUNV ZLWKRXW ERWWOHQHFNV
VHH WKH QHWZRUNV LQ )LJ ,Q DGGLWLRQ LW GRHV QRW ZRUN IRU
' QHWZRUNV
'' VHJPHQWDWLRQ DOJRULWKPV KDYH EHHQ VWXGLHG LQ
WKH FRPSXWHU YLVLRQ DQG JUDSKLFV DUHDV >@ ZKLFK WDUJHW
FRQWLQXRXV VKDSHV DQG XVH FHQWUDOL]HG VROXWLRQV 'HVSLWH WKH
UHVHPEODQFH WR WKRVH ZRUNV WKH SUREOHP ZH VWULYH WR DGGUHVV LV
PRUH FKDOOHQJLQJ EHFDXVH RI WKH QDWXUH RI D GLVWULEXWHG VHQVRU
QHWZRUN )LUVW WKH UDQGRP GHSOR\PHQW RI VHQVRU QRGHV PDNHV
WKH JHRPHWULF REMHFWV HJ KROHV QRW QHFHVVDULO\ IROORZ WKH
SURSHUWLHV RI WKHLU FRXQWHUSDUWV LQ D FRQWLQXRXV VSDFH 7KH
QDWXUH RI WKH UDQGRP GHSOR\PHQW DOVR PDNHV LW LPSUDFWLFDO WR
PDQXDOO\ LGHQWLI\ FRQYH[FRQFDYH UHJLRQV GXULQJ GHSOR\PHQW
RU H[WUDFW D JUDSK RI WKH QHWZRUN 6HFRQG LQ SUDFWLFH VHQVRU
QRGHV PD\ KDYH QR NQRZOHGJH RI ORFDWLRQ LQIRUPDWLRQ $V D
UHVXOW LQWHUQRGH GLVWDQFH LV RIWHQ HVWLPDWHG E\ VKRUWHVWSDWK
KRS FRXQW ZKRVH PHDVXUHPHQW DFFXUDF\ LV DGYHUVHO\ DIIHFWHG
E\ QHWZRUN FRQFDYLWLHV 7KLUG VLQFH WKH VHQVRU QHWZRUN LV
GLVFUHWH LW LV GLI¿FXOW RU LPSRVVLEOH WR GHFRPSRVH D VHQVRU
QHWZRUN LQWR VWULFWO\ FRQYH[ UHJLRQV GXH WR WKH ERXQGDU\
LUUHJXODULW\ ,W LV PRUH PHDQLQJIXO WR GHFRPSRVH WKH QHWZRUN
LQWR DSSUR[LPDWHO\ FRQYH[ UHJLRQV >@ >@ +RZHYHU KRZ WR
SURYLGH D ERXQG RI FRQYH[LW\ GHYLDWLRQ LV QRW VWUDLJKWIRUZDUG
B. Our Contributions
7KLV SDSHU SURSRVHV D QRYHO VHJPHQWDWLRQ VFKHPH XVLQJ
0RUVH IXQFWLRQ >@ OLQNLQJ WKH QRWLRQV RI FRQYH[ UHJLRQV
DQG WKH 5HHE JUDSK RI D QHWZRUN :H SURSRVH &216(/ IRU
&211QHFWLYLW\EDVHG 6(JPHQWDWLRQ LQ /DUJHVFDOH ''
VHQVRU QHWZRUNV ,Q &216(/ VHYHUDO ERXQGDU\ QRGHV ¿UVW
SHUIRUP ÀRRGLQJ WR FRQVWUXFW D Reeb graph 7KH RUGLQDU\ QRGHV
WKHQ FRPSXWH mutex pairs ORFDOO\ JHQHUDWLQJ D FRDUVH VHJPHQ
WDWLRQ OD\RXW 1H[W WKH QHLJKERU UHJLRQV WKDW DUH QRW PXWH[
SDLUV DUH PHUJHG )LQDOO\ E\ LJQRULQJ PXWH[ SDLUV WKDW OHDG
WR VPDOO FRQFDYLWLHV ZH SURYLGH D FRQ¿JXUDEOH ERXQG IRU WKH
-,$1* et al. &211(&7,9,7<%$6(' 6(*0(17$7,21 ,1 /$5*(6&$/( '' 6(1625 1(7:25.6
)LJ D 0RUVH IXQFWLRQ DQG OHYHO VHWV
E /HYHO VHWV RI D ' QHWZRUN
DQG
DUH WZR /FRPSRQHQWV RI
VXEQHWZRUNV
GHYLDWLRQ IURP FRQYH[LW\ &216(/ LV GHVLUDEOH
FRPSDUHG WR SUHYLRXV VROXWLRQV LW ZRUNV IRU ERWK ' DQG
' VHQVRU QHWZRUNV LW XVHV PHUHO\ QHWZRUN FRQQHFWLYLW\
LQIRUPDWLRQ LW SURYLGHV D ERXQG RQ D UHJLRQ
V GHYLDWLRQ IURP
FRQYH[LW\ $GGLWLRQDOO\ &216(/ ZRUNV IRU D YDULHW\ RI UDGLR
PRGHOV LQFOXGLQJ WKH TXDVL8'* PRGHO ORJQRUPDO PRGHO
DQG WKH SUREDELOLVWLF FRQQHFWLYLW\ PRGHO &216(/ LV IXOO\
GLVWULEXWHG DQG LV VFDODEOH DV LWV WLPH DQG PHVVDJH FRPSOH[LWLHV
DUH ERWK OLQHDU ZLWK QHWZRUN VL]H ([WHQVLYH VLPXODWLRQV VKRZ
WKDW &216(/ ZRUNV ZHOO LQ WKH SUHVHQFH RI KROHV DQG VKDSH
YDULDWLRQ DOZD\V \LHOGLQJ DSSURSULDWH VHJPHQWDWLRQ UHVXOWV
)XUWKHUPRUH ZH SURSRVH WR LQWHJUDWH QHWZRUN VHJPHQWDWLRQ
ZLWK H[LVWLQJ DSSOLFDWLRQV VXFK DV JHRJUDSKLF URXWLQJ DQG
FRQQHFWLYLW\EDVHG ORFDOL]DWLRQ DQG HYDOXDWH WKHLU SHUIRUPDQFH
LQ 6HFWLRQ 9,
7KH UHPDLQGHU RI WKH SDSHU SURFHHGV DV IROORZV
6HFWLRQ ,, JLYHV WKH EDFNJURXQG RI 0RUVH IXQFWLRQV DQG 5HHE
JUDSK 6HFWLRQ ,,, LV GHYRWHG WR D GHVFULSWLRQ RI &216(/
DOJRULWKP 6HFWLRQ ,9 GLVFXVVHV WKH FRPSOH[LW\ RI &216(/
:H HYDOXDWH RXU &216(/ LQ 6HFWLRQ 9 6HFWLRQ 9, SURSRVHV
WZR LQWHUHVWLQJ SURWRFROV WKDW LQWHJUDWH VKDSH VHJPHQWDWLRQ
ZLWK H[LVWLQJ DSSOLFDWLRQV )LQDOO\ 6HFWLRQ 9,, FRQFOXGHV WKH
SDSHU
,, 35(/,0,1$5,(6
A. Morse Functions and Reeb Graph
1) Morse Functions: )RU D PDQLIROG D 0RUVH IXQFWLRQ >@
ZKHUH LV WKH VHW RI UHDO QXPEHUV
LV D PDSSLQJ
7KH PDSSLQJ FDQ EH FRQVLGHUHG DV D SURMHFWLRQ IURP KLJKGL
PHQVLRQDO WR RQHGLPHQVLRQDO PDQLIROG ,Q D GLVFUHWH QHWZRUN
WKH 0RUVH IXQFWLRQ LV FRQVWUXFWHG DV IROORZV )LUVW ZH VHOHFW
DQ origin node WKHQ HYHU\ RWKHU QRGH REWDLQV LWV KRSFRXQW
GLVWDQFH GHQRWHG E\
WR QRGH 7KLV SURFHVV HVWDEOLVKHV D
ZKHUH LV WKH VHW RI QRQQHJDWLYH LQWH
PDSSLQJ
JHUV ,Q )LJ WKH QRGHV RQ WKH VDPH DUF KDYH DQ HTXDO YDOXH RI
WKH 0RUVH IXQFWLRQ ,W LV QRWHG WKDW WKH 0RUVH IXQFWLRQ LV PRUH
JHQHUDO WKDW WKH OHYHO RI QRGHV RQ WKH VKRUWHVW SDWK WUHH 0RUH
RYHU LW LV XVHIXO WR SURFHHG RQ RXU GHVFULSWLRQ RI 5HHE JUDSK
ZKHUH ZH KDYH WR PDNH XVH RI WKH LQYHUVH IXQFWLRQ RI 0RUVH
IXQFWLRQ /HW
EH WKH VHW RI QRGHV FDOOHG WKH WK level
set ZKRVH 0RUVH IXQFWLRQ YDOXHV DUH )RU H[DPSOH DOO WKH
QRGHV RQ WKH JUHHQ DUF LQ )LJ D VKDUH WKH VDPH 0RUVH IXQF
WLRQ YDOXH 7KH ]HURWK OHYHO VHW
FRQWDLQV WKH RULJLQ
QRGH RQO\
)LJ 5HHE JUDSKV UHG QRGHV DQG OLQHV RI WZR QHWZRUN WRSRORJLHV *UHHQ
GDVKHG DUFV UHSUHVHQW FXWV
2) Reeb Graph: 7KH 5HHE JUDSK >@ LV FRQVWUXFWHG EDVHG RQ
WKH 0RUVH IXQFWLRQ RI D QHWZRUN *LYHQ D 0RUVH IXQFWLRQ HDFK RI LWV OHYHO VHWV FRQVLVWV RI D QXPEHU RI FRQQHFWHG FRP
SRQHQWV FDOOHG level components /FRPSRQHQWV IRU VKRUW VHH
)LJ D IRU DQ H[DPSOH ,Q DQ /FRPSRQHQW
DW OHYHO
HDFK QRGH KDV D QXPEHU RI QHLJKERUV LQ WKH
WK OHYHO
LV UHIHUUHG WR QRGHV DW OHYHO DQG WKH RULJLQ QRGH LV WKH QRGH 7KDW LV DOO QRGHV LQ DUH KRSV DZD\ IURP WKH RULJLQ QRGH 7KH
VHW RI VXFK DERYHPHQWLRQHG QHLJKERUV LV FDOOHG V children
set GHQRWHG E\
$V D UHVXOW WKH /FRPSRQHQWV H[SDQG DV
WKH OHYHO QXPEHU JURZV 7KHUH DUH WKUHH EDVLF W\SHV RI HYHQWV
GXULQJ WKH WUDQVLWLRQ IURP RQH /FRPSRQHQW WR LWV FKLOGUHQ VHW
IRU VLPSOLFLW\ RI H[SRVLWLRQ ZH RPLW FRPSRVLWH HYHQWV
Extend event
LV D PD[LPDO /FRPSRQHQW LQ WKH
WK OHYHO
Split event
FRQWDLQV WZR RU PRUH /FRPSRQHQWV LQ
WK OHYHO
WKH
Merge event
LV D VXEVHW RI DQ /FRPSRQHQW LQ WKH
WK OHYHO ZKLFK PHDQV WKDW PXOWLSOH /FRPSRQHQWV LQ
WKH WK OHYHO VKDUH WKH VDPH FRQQHFWHG FKLOGUHQ VHW
$ VHULHV RI H[WHQG HYHQWV PD\ WDNH SODFH LQ VXFFHVVLRQ >VD\
WKH /FRPSRQHQWV IURP OHYHO WR OHYHO LQ )LJ D@ DQG WKH
LQYROYHG /FRPSRQHQWV ZLOO IRUP D FRQQHFWHG PXOWLOHYHO FRP
SRQHQW RI WKH QHWZRUN FDOOHG D Reeb component $ YHUWH[ LQ
WKH ¿QDO 5HHE JUDSK RU D Reeb vertex UHSUHVHQWV D PD[LPDO
5HHE FRPSRQHQW DQG DQ HGJH LQ WKH 5HHE JUDSK RU D Reeb
edge UHÀHFWV WKH VSOLW RU PHUJH HYHQWV ,QLWLDOO\ WKH 5HHE JUDSK
LV HPSW\ 7KH ]HURWKOHYHO VHW
ZKLFK FRQWDLQV RQO\ WKH
RULJLQ QRGH DQG WKXV D VLQJOH /FRPSRQHQW WULJJHUV WKH JHQHUD
WLRQ RI WKH ¿UVW 5HHE YHUWH[ 7KLV YHUWH[ FRQWLQXHV WR UHSUHVHQW
WKH GHVFHQGDQW /FRPSRQHQWV XQWLO D VSOLW RU PHUJH HYHQW KDS
SHQV )RU D VSOLW HYHQW >VD\ WKH /FRPSRQHQWV IURP OHYHO WR
OHYHO LQ )LJ D@ LW PHDQV WKDW DQ /FRPSRQHQW
KDV H[
SDQGHG LQWR
/FRPSRQHQWV LQ ZKLFK FDVH QHZ 5HHE
YHUWLFHV ZLOO EH JHQHUDWHG DV FKLOGUHQ RI LQ WKH 5HHE JUDSK
:KHQ D PHUJH HYHQW KDSSHQV LW PHDQV WKDW PXOWLSOH /FRP
SRQHQWV VKDUH WKH VDPH FRQQHFWHG FKLOGUHQ VHW VR D QHZ 5HHE
YHUWH[ ZLOO EH JHQHUDWHG WR UHSUHVHQW WKLV FKLOGUHQ VHW VHUYLQJ DV
WKH FRPPRQ FKLOG RI WKRVH /FRPSRQHQWV
FRUUHVSRQGLQJ 5HHE
YHUWLFHV
)LJ D VKRZV DQ H[DPSOH RI WKH 5HHE JUDSK UHG QRGHV DQG
HGJHV FRUUHVSRQGLQJ WR WKH QHWZRUN LQ )LJ D ,Q )LJ D
IURP
WR
WKHUH H[LVWV D VSOLW HYHQW $V VXFK WZR
DQG
DUH JHQHUDWHG XQGHU WKH RULJLQDO
QHZ 5HHE YHUWLFHV
YHUWH[ ZKLFK UHSUHVHQWV WKH XQLRQ RI
WKURXJK
)LJ E VKRZV DQRWKHU H[DPSOH RI 5HHE JUDSK FRUUHVSRQGLQJ
WR D QHWZRUN GHSOR\HG LQ D ' ULQJ ,Q WKLV ¿JXUH WZR 5HHE
YHUWLFHV DQG DUH PHUJHG LQWR D QHZ 5HHE YHUWH[ *HQHUDOO\ D VSOLW HYHQW KDSSHQV ZKHQ D concave node
HPHUJHV >@ GXULQJ WKH H[SDQGLQJ SURFHVV RI /FRPSRQHQWV
+HUH D FRQFDYH QRGH >VHH
LQ )LJ D@ LV D QRGH ZKHUH
WKH LQZDUG DQJOH LH WKH DQJOH VSDQQLQJ DFURVV WKH VHQVLQJ
DUHD LV JUHDWHU WKDQ >@ $ PHUJH HYHQW KDSSHQV ZKHQ WKH
QHWZRUN WRSRORJ\ IRUPV D ORRS %\ FDSWXULQJ WKH VSOLWWLQJ DQG
ORRSLQJ EHKDYLRU WKH 5HHE JUDSK FUHDWHV D XVHIXO DEVWUDFWLRQ
RI WKH RULJLQDO QHWZRUN WRSRORJ\
DQG
DUH FDOOHG cuts GH
,Q )LJ WKH OLQHV
¿QHG DV WKH QHZ /FRPSRQHQWV DULVLQJ LQ WKH VSOLW HYHQW RU WKH
QHZ FKLOGUHQ VHW JHQHUDWHG E\ WKH PHUJH HYHQW 7KH FXWV DUH
PHDQW WR VHSDUDWH WKH UHJLRQV ,Q )LJ D IRU H[DPSOH WKH
WZR FXWV
DQG
SDUWLWLRQ WKH QHWZRUN LQWR WKUHH
UHJLRQV
B. Approximate Convexity
)RU PRVW DSSOLFDWLRQV D VWULFWO\ FRQYH[ VHJPHQWDWLRQ LV XQ
QHFHVVDU\ >@ >@ 7KHUHIRUH ZH DLP DW SDUWLWLRQLQJ WKH QHW
ZRUN LQWR approximately convex UHJLRQV 7R WKDW HQG ZH GH¿QH
DQ straight line DV IROORZV
Denition 1 ( -Straight Path): $ SDWK EHWZHHQ WZR QRGHV
DQG LV FDOOHG DQ straight path LI DQG RQO\ LI DQ\ QRGH RQ
WKH SDWK LV DW PRVW
DZD\ IURP WKH (XFOLGHDQ VWUDLJKW OLQH
EHWZHHQ DQG ZKHUH
LV WKH UDGLR UDQJH RI VHQVRU QRGHV
,W LV QRWHG WKDW WKH WHUP ³WKH UDGLR UDQJH´ LV XVHG LQ
'H¿QLWLRQ VLQFH KHUH WZR QRGHV DUH DVVXPHG WR EH DEOH WR
FRPPXQLFDWH ZLWKLQ WKH UDGLR UDQJH 7KH FRQFHSW RI FRQYH[
UHJLRQV WKXV IROORZV
Denition 2 ( -Convex Region): $ QHWZRUN UHJLRQ LV FDOOHG
DQ convex region LI ZLWKLQ WKDW UHJLRQ IRU DQ\ WZR QRGHV
DQG WKHUH DOZD\V H[LVWV DQ VWUDLJKW SDWK FRQQHFWLQJ WKHP
DQG DOO WKH QRGHV RQ WKDW SDWK EHORQJ WR WKH UHJLRQ
:KHQ WKH QHWZRUN LV VHJPHQWHG LQWR VHYHUDO UHJLRQV HDFK
UHJLRQ LV DSSUR[LPDWHO\ FRQYH[ RU FRQYH[ )RU H[DPSOH LQ
)LJ OHW
DQG
7KH GLV
WDQFH IXQFWLRQ
LV D PDSSLQJ IURP WZR QRGHV WR WKH UHDO
QXPEHU VHW 7R VDWLVI\ WKH FRQGLWLRQ RI FRQYH[LW\ ZH VKRXOG
KDYH
7KDW LV
:KHQ
WKLV FRQGLWLRQ DOZD\V KROGV
C. Mutex Pairs
,Q D FRQWLQXRXV VSDFH LI DQ DUHD LV FRQYH[ WKHQ LW FRQWDLQV
WKH OLQH VHJPHQW EHWZHHQ HYHU\ SDLU RI LWV LQQHU SRLQWV 7KLV
IDFW PRWLYDWHV XV WR FRQVLGHU WKH UHODWLRQ EHWZHHQ LQQHU SRLQWV
RI D QHWZRUN LQ WKH OLJKW RI 0RUVH IXQFWLRQV +HUH ZH XVH WKH
WHUP ³PXWH[´ WR LQGLFDWH WKDW WZR QRGHVSDUWV FDQ QRW EH LQ RQH
FRQYH[ UHJLRQ
Denition 3 (Morse Path): *LYHQ D QHWZRUN DQG D 0RUVH
IXQFWLRQ D Morse path EHWZHHQ WZR QRGHV
DQG
LV D SDWK
RQ ZKLFK DOO QRGHV KDYH WKH VDPH 0RUVH IXQFWLRQ YDOXH
Denition 4 (Mutex Pair): *LYHQ D QHWZRUN DQG D 0RUVH
IXQFWLRQ WZR QRGHV
DQG DUH FDOOHG D mutex pair GHQRWHG
LI WKHUH H[LVWV QR 0RUVH SDWK EHWZHHQ WKHP
E\
,Q )LJ LW LV HDV\ WR ¿QG D QRGH LQ DUHD
DQG D QRGH LQ
DUHD WKDW IRUP D PXWH[ SDLU ,QWXLWLYHO\ DIWHU VHJPHQWDWLRQ
,((($&0 75$16$&7,216 21 1(7:25.,1* 92/ 12 )(%58$5< WKH\ VKRXOG QRW EH LQ WKH VDPH UHJLRQ )RU WZR GLVMRLQW UHJLRQV
DQG LI WKHUH LV D PXWH[ SDLU IRUPHG E\ D QRGH IURP
DQG D QRGH IURP WKHQ DQG
DUH FDOOHG D PXWH[ SDLU DV
ZHOO GHQRWHG E\
1RWH WKDW D QRGH FDQ EH UHJDUGHG DV D
VLQJOHWRQ VHW VR D PXWH[ SDLU RI UHJLRQV LQ IDFW LQFOXGHV D PXWH[
SDLU RI QRGHV
*LYHQ WKH 5HHE JUDSK FRQVWUXFWHG IURP WKH 5HHE FRPSR
QHQWV FRUUHVSRQGLQJ WR DQ\ WZR YHUWLFHV DUH D PXWH[ SDLU $
PXWH[ SDLU IRUPHG E\ WZR DGMDFHQW 5HHE FRPSRQHQWV LV VHS
DUDWHG E\ WKH FXWV EHWZHHQ WKH WZR 5HHE FRPSRQHQWV
1H[W ZH H[WHQG WKH GH¿QLWLRQV RI 0RUVH SDWK DQG PXWH[ SDLU
E\ LQWURGXFLQJ DSSUR[LPDWLRQ
Denition 5 ( -Morse Path): *LYHQ D QHWZRUN DQG D
0RUVH IXQFWLRQ WZR QRGHV
DQG
ZLWK HTXDO 0RUVH
IXQFWLRQ YDOXHV KDYH D Morse path EHWZHHQ WKHP LI WKH
SDWK FRQWDLQV WZR LQWHUPHGLDWH QRGHV
DQG
VXFK WKDW
WKHUH H[LVWV D 0RUVH SDWK EHWZHHQ DQG
DQG DQG
Denition 6 ( -Mutex Pair): *LYHQ D QHWZRUN DQG D 0RUVH
IXQFWLRQ WZR QRGHV DQG ZLWK WKH VDPH 0RUVH IXQFWLRQ
YDOXHV DUH FDOOHG D mutex pair GHQRWHG E\
LI WKHUH
H[LVWV QR 0RUVH SDWK EHWZHHQ WKHP
'H¿QLWLRQ DOORZV D VPDOO SDUW RI QRQFRQYH[ VXEUHJLRQV WR
EH PHUJHG ¿QDOO\ 2YHUDOO DQG FDQ EH FRQVLGHUHG DV WZR
SDUDPHWHUV DOORZLQJ WKH QHWZRUN RSHUDWRU WR FRQWURO WKH OHYHO
RI FRQYH[LW\ RI JHQHUDWHG QHWZRUN VHJPHQWV $V VXFK RXU DO
JRULWKP LV WR JHQHUDWH D VHW RI
FRQYH[ UHJLRQV 7KDW
LV &216(/ HQVXUHV D ERXQG IRU WKH UHJLRQV
GHYLDWLRQ IURP
FRQYH[LW\
,,, &216(/ $/*25,7+0
,Q WKLV VHFWLRQ ZH SUHVHQW WKH LPSOHPHQWDWLRQ GHWDLOV RI WKH
VHJPHQWDWLRQ DOJRULWKP ,W LV QRWHG WKDW HYHQ LQ D ' GRPDLQ
FRPSXWLQJ D PLQLPXP QXPEHU RI FRQYH[ FRPSRQHQWV IRU D
SRO\JRQ ZLWK KROHV LV 13KDUG >@ :H WKHUHIRUH GR QRW SXUVXH
DQ RSWLPDO FRQYH[ VHJPHQWDWLRQ ,QVWHDG RXU JRDO LV WR SURYLGH
D VLPSOH DQG SUDFWLFDO DOJRULWKP WKDW FDQ EH SHUIRUPHG LQ D GLV
WULEXWHG ZD\
A. Establishing the Morse Function
,Q WKH ¿UVW VWHS ZH UDQGRPO\ FKRRVH QRGHV URXJKO\ RQ
WKH RXWHU ERXQGDU\ RI WKH QHWZRUN :H XVH D WHFKQLTXH VLP
LODU WR WKH RQH LQ >@ $Q DUELWUDU\ QRGH ÀRRGV WKH QHWZRUN
WR ¿QG WKH IDUWKHVW QRGH
WR 7KHUHDIWHU
ÀRRGV WKH QHW
ZRUN WR ¿QG WKH IDUWKHVW
WR LWVHOI 7KHQ
LV WKH QRGH WKDW
KDV WKH PD[LPXP VXP RI WKH VTXDUH URRWV RI WKH KRS FRXQWV
IURP WKH QRGHV DQG 7KLV SURFHVV FRQWLQXHV XQWLO QRGHV
DUH REWDLQHG RQ WKH RXWHU ERXQGDU\ 1RWH WKDW
WKLV VHOHFWLRQ SKDVH ZRUNV ZHOO IRU ERWK '' QHWZRUNV
1H[W HDFK RI WKH QRGHV RQ WKH ERXQGDU\ ÀRRGV WKH QHW
ZRUN 7KH JRDO RI WKH ÀRRGLQJ RSHUDWLRQV LV WZRIROG )LUVW DIWHU
D ÀRRGHG PHVVDJH IURP UHDFKHV D QRGH
UHFRUGV WKH SDUHQW
IURP ZKLFK LW UHFHLYHV WKH PHVVDJH DV ZHOO DV WKH KRS FRXQW
WR WKH QRGH %\ GRLQJ VR WKH QRGH KDV WKH NQRZOHGJH RI
FRUUHVSRQGLQJ WR
WKH 0RUVH IXQFWLRQ YDOXH
6HFRQG WKH ÀRRGLQJ DOORZV XV WR FRQVWUXFW WKH
5HHE JUDSK LQ D GLVWULEXWHG ZD\ DV GHVFULEHG LQ 6HFWLRQ ,,,%
-,$1* et al. &211(&7,9,7<%$6(' 6(*0(17$7,21 ,1 /$5*(6&$/( '' 6(1625 1(7:25.6
B. Constructing the Reeb Graph
7KH NH\ WR FRQVWUXFWLQJ D 5HHE JUDSK LV WR LGHQWLI\ WKH 5HHE
FRPSRQHQWV DQG VHOHFW D Reeb landmark node RU 5HHE ODQG
PDUN IRU HDFK RI WKHP UHSUHVHQWLQJ D 5HHE YHUWH[ 7R WKLV HQG
HDFK QRGH ZLOO EH DVVLJQHG D Reeb component ID ZKLFK LV HTXDO
WR WKH ,' RI LWV ODQGPDUN QRGH :KHQ QR FRQIXVLRQ RFFXUV ZH
XVH WKH ,' WR UHIHU WR D QRGH ,Q DGGLWLRQ HDFK 5HHE ODQGPDUN
DOVR PDLQWDLQV D VHW RI 5HHE HGJHV FRQQHFWLQJ WR WKH ODQGPDUNV
RI QHLJKERULQJ 5HHE FRPSRQHQWV
,Q WKH FRQVWUXFWLRQ RI WKH 5HHE JUDSK ZH ZLOO RIWHQ XVH WZR
SULPLWLYH URXWLQHV
L-Component Landmark Election: 7KH QRGHV LQ HDFK /FRP
SRQHQW HOHFW D OHDGHU FDOOHG WKH /FRPSRQHQW
V landmark 7R GR
VR HDFK QRGH LQ WKH /FRPSRQHQW GHFODUHV LWVHOI WR EH D ODQG
PDUN ZLWK D SUHGH¿QHG SUREDELOLW\ DQG EURDGFDVW WR LWV QHLJK
ERUV ,I D QRGH GRHV QRW VHOHFW LWVHOI WR EH D ODQGPDUN DQG GRHV
QRW UHFHLYH DQ\ EURDGFDVW PHVVDJH ZLWKLQ D SUHGH¿QHG SHULRG
RI WLPH LW GHFODUHV LWVHOI WR EH D ODQGPDUN ZLWK WKH VDPH SURE
DELOLW\ DJDLQ 7KLV SURFHVV FRQWLQXHV XQWLO HDFK QRGH UHFHLYHV D
EURDGFDVW PHVVDJH :KHQ PXOWLSOH QRGHV LQ WKH VDPH FRPSR
QHQW FRPSHWH WR EH D ODQGPDUN WKH QRGH ZLWK D ODUJHU ,' ZLOO
SUHYDLO ,Q WKH HQG HDFK /FRPSRQHQW ZLOO KDYH HOHFWHG D ODQG
PDUN ZKRVH ,' LV UHFRUGHG E\ HDFK QRGH LQ WKLV /FRPSRQHQW
Neighboring L-Components Discovery: 5HFDOO WKDW JLYHQ DQ
/FRPSRQHQW LWV FKLOGUHQ LQ WKH
WK OHYHO FRQVWLWXWH
D children set RI /LNHZLVH WKH SDUHQW QRGHV RI DQ /FRP
LQ WKH
WK OHYHO FRQVWLWXWH V parent set $Q
SRQHQW
V
/FRPSRQHQW ODQGPDUN ÀRRGV LWV FRPSRQHQW DVNLQJ DOO QRGHV
WR FRQWDFW WKHLU QHLJKERUV LQ D VSHFL¿HG QHLJKERULQJ OHYHO 7KRVH
QHLJKERUV UHWXUQ WKHLU RZQ /FRPSRQHQW ,'V WR WKH UHTXHVWLQJ
QRGHV ZKLFK LQ WXUQ UHSRUW WKH FROOHFWHG /FRPSRQHQW ,'V WR ,Q WKH EHJLQQLQJ DQ /FRPSRQHQW LQ WKH ¿UVW OHYHO VHW FRQ
VWLWXWHV D WHPSRUDU\ 5HHE FRPSRQHQW 6XSSRVH DW WKH FXUUHQW
VWDJH D 5HHE FRPSRQHQW KDV HOHFWHG D 5HHE ODQGPDUN DQG RQH
RI LWV /FRPSRQHQWV DW WKH PD[LPXP OHYHO
KDV D FKLOGUHQ
7KURXJK WKH QHLJKERULQJ /FRPSRQHQWV GLVFRYHU\
VHW
URXWLQH
DQG
PRUH SUHFLVHO\ WKHLU ODQGPDUN QRGHV
PD\ ¿QG WKHPVHOYHV LQ RQH RI WKH IROORZLQJ VLWXDWLRQV
([WHQG HYHQW KDV RQO\ RQH QHLJKERULQJ /FRPSRQHQW
LQ
DQG
KDV RQO\ RQH QHLJKERULQJ /FRPSR
QHQW LQ LWV SDUHQW VHW
6SOLW HYHQW
KDV PRUH WKDQ RQH QHLJKERULQJ /FRPSR
QHQWV LQ
ZKLFK DOO KDYH RQO\ RQH SDUHQW VHW
0HUJH HYHQW
KDV RQO\ RQH QHLJKERULQJ /FRPSRQHQW
DQG
KDV PRUH WKDQ RQH QHLJKERULQJ /FRP
LQ
SRQHQWV LQ LWV SDUHQW VHW
)LJ D VKRZV DQ H[DPSOH RI WKH ¿UVW FDVH ZKHUH WKHUH DUH
WZR /FRPSRQHQWV ZKRVH QRGHV KDYH 5HHE FRPSRQHQW ,'
DQG 7KH WZR /FRPSRQHQWV HDFK KDYH D VLQJOH QHLJKERULQJ
/FRPSRQHQW OHG E\ ODQGPDUNV
DQG UHVSHFWLYHO\ LQ WKH
QH[W OHYHO 7KXV WKH QRGHV LQ WKH /FRPSRQHQWV OHG E\ DQG
ZLOO VHW WKHLU 5HHE FRPSRQHQW ,' WR WKDW RI WKHLU SDUHQWV LH
HLWKHU
RU )LJ E VKRZV DQ H[DPSOH RI WKH VHFRQG FDVH ZKHUH WKH
/FRPSRQHQW OHG E\ ODQGPDUN KDV WZR QHLJKERULQJ /FRP
SRQHQWV LQ WKH QH[W OHYHO OHG E\ ODQGPDUN QRGHV
DQG UHVSHFWLYHO\ 7KXV WZR QHZ 5HHE FRPSRQHQWV UHSUHVHQWHG E\
DQG UHVSHFWLYHO\ DUH JHQHUDWHG $OVR WKH HGJHV
)LJ /RFDO 5HHE JUDSK D ([WHQG HYHQW E 6SOLW HYHQW F 0HUJH HYHQW
DQG
DUH JHQHUDWHG DQG UHFRUGHG E\ WKH WKUHH HQG QRGHV
DQG )LJ F VKRZV DQ H[DPSOH RI WKH WKLUG FDVH ZKHUH WKH
/FRPSRQHQWV OHG E\ ODQGPDUNV
DQG
KDYH WKH VDPH
QHLJKERULQJ /FRPSRQHQW LQ WKH QH[W OHYHO 7KXV D QHZ 5HHE
FRPSRQHQW UHSUHVHQWHG E\
LV JHQHUDWHG $OVR WKH HGJHV
DQG
DUH JHQHUDWHG DQG UHFRUGHG E\ WKH WKUHH
HQG QRGHV
7R JXDUDQWHH D ERXQG RQ DQ /FRPSRQHQW
V GHYLDWLRQ IURP
FRQYH[LW\ WKH FRQGLWLRQ RI
VKRXOG EH VDWLV¿HG
DV ZH GLVFXVVHG LQ 6HFWLRQ ,,% 2WKHUZLVH DQ /FRPSRQHQW
VKRXOG EH SDUWLWLRQHG 6SHFL¿FDOO\ ZH LGHQWLI\ WZR QRGHV VD\
DQG WKDW KDYH WKH ORQJHVW SDWK OHQJWK LQ LW DQG WKH QRGHV
FORVHU WR WKDQ WR
IRUP D UHJLRQ DQG WKH UHPDLQLQJ QRGHV
IRUP DQRWKHU UHJLRQ 7KH FRQGLWLRQ ZLOO EH H[DPLQHG DJDLQ IRU
HDFK UHJLRQ XQWLO WKH FRQYH[LW\ FRQGLWLRQ LV VDWLV¿HG
)LQDOO\ DOO 5HHE ODQGPDUNV VHQG WKHLU ORFDO WRSRORJLHV EDFN
WR WKH RULJLQ IROORZLQJ V ÀRRGLQJ WUHH $IWHU WKLV SKDVH
WKH RULJLQ KDV WKH IXOO SLFWXUH RI WKH 5HHE JUDSK )LJ D DQG
E VKRZV WKH UHVXOW RI WKH 5HHE JUDSK DIWHU WKH ÀRRGLQJ IRU D
0RUVH IXQFWLRQ ,Q )LJ D WKH QRGHV PDUNHG ZLWK WKH VDPH
FRORU DUH LQ WKH VDPH UHJLRQ FRUUHVSRQGLQJ WR D YHUWH[ LQ 5HHE
JUDSK
,W LV QRWHG WKDW ZH KDYH UDQGRPO\ FKRRVHQ QRGHV DV RULJLQ
QRGHV 7KHUHIRUH EHVLGHV WKH 5HHE JUDSK VKRZQ LQ )LJ E
WKHUH DUH
DGGLWLRQDO 5HHE JUDSKV REWDLQHG LQ D VLPLODU ZD\
C. Identifying Mutex Pairs and Coarse Segmentation
$OWKRXJK D 5HHE JUDSK LV GH¿QHG DV D XQGLUHFWHG JUDSK HDFK
RI LWV HGJHV FDQ DFWXDOO\ EH DVVLJQHG D GLUHFWLRQ IROORZLQJ WKH
JHQHUDWLRQ RUGHU RI 5HHE YHUWLFHV 7KHUHIRUH ZH FDQ VD\ WKDW D
5HHE YHUWH[ LV WKH DQFHVWRU RI DQRWKHU 5HHE YHUWH[ LI DQG RQO\
LI WKHUH LV D GLUHFWHG SDWK EHWZHHQ WKHP LQ WKH 5HHE JUDSK
0XWH[ SDLUV DUH LGHQWL¿HG ZLWK WKH IROORZLQJ REVHUYDWLRQ
,I WZR 5HHE YHUWLFHV DUH QRW LQ DQ DQFHVWRU±GHVFHQGDQW UHOD
WLRQVKLS WKHQ WKHLU FRUUHVSRQGLQJ 5HHE FRPSRQHQWV DQG 5HHE
ODQGPDUNV IRUP D PXWH[ SDLU 7KLV LV EHFDXVH LI WZR 5HHE FRP
SRQHQWV DUH QRW LQ VXFK D UHODWLRQVKLS WKHQ DQ\ SDWK EHWZHHQ
WKHP PXVW SDVV D FRPPRQ DQFHVWRU 5HHE FRPSRQHQW ZKLFK
PDNHV WKH SDWK QRW VWUDLJKW )RU H[DPSOH LQ )LJ DQG
DUH D PXWH[ SDLU EXW
DQG
DUH QRW $W WKH VDPH WLPH
WKH FXWV EHWZHHQ WKH DGMDFHQW 5HHE YHUWLFHV FDQ VHSDUDWH WKHVH
PXWH[ SDLUV
$V LQWURGXFHG HDUOLHU DOO QRGHV LQ WKH VDPH 5HHE FRPSR
QHQW VKRXOG KDYH UHFRUGHG WKHLU 5HHE ODQGPDUN
V ,' 6LQFH
WKHUH DUH RULJLQ QRGHV WKHUH DUH 5HHE JUDSKV FRQVWUXFWHG
$V D UHVXOW HDFK QRGH UHFRUGV D VHW RI
5HHE ODQGPDUN
DQG WKHUH DUH IRXU 5HHE YHUWLFHV
,'V ,Q )LJ D
LQ HDFK 5HHE JUDSK FRUUHVSRQGLQJ WR 5HHE ODQGPDUNV
,((($&0 75$16$&7,216 21 1(7:25.,1* 92/ 12 )(%58$5< )LJ 6WHSV RI WKH &216(/ DOJRULWKP D E 5HHE JUDSK FRQVWUXFWLRQ F &RDUVH VHJPHQWDWLRQ OD\RXW G 0HUJLQJ UHVXOW 7KH ¿QDO UH¿QHG UHVXOW LV LQ )LJ F
+HUH HDFK QRGH
PDLQWDLQV D VHW RI HLJKW 5HHE ODQGPDUN ,'V
7KH EDVLF LGHD RI FRDUVH VHJPHQWDWLRQ LV WKDW DQ\ SDLU RI
QRGHV ZLWK D GLIIHUHQW VHW RI 5HHE ODQGPDUN ,'V VKRXOG EH LQ
GLIIHUHQW UHJLRQV 7DNLQJ WKH QHWZRUN LQ )LJ DV DQ H[DPSOH
DVVXPH WKH 5HHE ODQGPDUNV DUH
(DFK RI WKHP
SHUIRUPV ÀRRGLQJ ZLWK LWV RZQ ,' WR UHSUHVHQW D UHJLRQ GH
QRWHG E\
DV ZHOO DV LWV VHW RI HLJKW 5HHE
ODQGPDUN ,'V +HUHLQDIWHU LV FDOOHG D representative RI D UH
JLRQ LI
:KHQ D QRGH UHFHLYHV D ÀRRGHG
PHVVDJH LW FRPSDUHV WKH UHFHLYHG VHW RI HLJKW 5HHE ODQGPDUN
,'V WR LWV RZQ VHW RI 5HHE ODQGPDUN ,'V :KHQ WKH\ DUH GLI
IHUHQW RU ZKHQ KDV DOUHDG\ KDG D UHJLRQ ,'
GLVFDUGV WKH PHVVDJH 2WKHUZLVH XSGDWHV LWV UHJLRQ ,' DV
DQG WKHQ IRUZDUGV WKH PHVVDJH WR DOO LWV
QHLJKERUV
1RW DOO WKH 5HHE ODQGPDUNV ZLOO EHFRPH UHJLRQDO UHSUH
VHQWDWLYHV EHFDXVH VRPH RI WKHP PD\ KDYH WKH VDPH VHW RI ODQG
PDUN ,'V ,Q DGGLWLRQ VRPH UHJLRQV PD\ ¿QG QR UHSUHVHQWDWLYH
VLQFH WKH\ PD\ QRW FRQWDLQ D 5HHE ODQGPDUN 7R DGGUHVV WKLV
SUREOHP HDFK RI WKH UHPDLQLQJ QRGHV VD\ QRGH WKDW VWLOO
KDYH QRW EHHQ DVVLJQHG D UHJLRQ ,' ZLOO DV\QFKURQRXVO\ GHFODUH
LWVHOI WR EH D UHSUHVHQWDWLYH DQG WKHQ EURDGFDVW WR DOO LWV QHLJK
ERUV WKDW KDYH WKH VDPH VHW RI ODQGPDUN ,'V :KHQ D QRGH
UHFHLYHV WKLV PHVVDJH LW DJDLQ FRPSDUHV
DQG
2QO\ ZKHQ
WKH QRGH XSGDWHV LWV UHJLRQ
DQG IRUZDUGV WKLV PHVVDJH FRQWDLQLQJ
,' DV
,Q WKH HQG HYHU\ QRGH KDV D UHJLRQ ,' DQG HDFK UHJLRQ KDV
D UHSUHVHQWDWLYH ZKLFK PDLQWDLQV WKH LQIRUPDWLRQ RI WKH 5HHE
ODQGPDUN ,'V DV ZHOO DV WKH 5HHE JUDSKV $OO UHJLRQV DUH
WKH UHVXOW RI WKH coarse segmentation RI WKH VHQVRU QHWZRUN
)LJ F VKRZV D UHVXOW RI FRDUVH VHJPHQWDWLRQ RI WKH QHWZRUN
ZKHUH VXEUHJLRQV DUH JHQHUDWHG
D. Merging Regions
7KH FXWV LQGXFHG IURP WKH 0RUVH IXQFWLRQ ZLOO RIWHQ JHQHUDWH
WRR PDQ\ UHJLRQV )RU LQVWDQFH DV PDQ\ DV UHJLRQV DUH JHQ
HUDWHG LQ )LJ F )RU WKH SXUSRVH RI FRQYH[ VHJPHQWDWLRQ ZH
RQO\ QHHG WR VHOHFW VRPH FXWV WR VDWLVI\ DOO PXWH[ SDLUV
7KH SURFHVV RI FXWV VHOHFWLRQ LV FDOOHG merging regions (DFK
UHSUHVHQWDWLYH QRGH LQ WKH UHJLRQ PDLQWDLQV D ODQGPDUN ,' OLVW
7KH UHSUHVHQWDWLYH QRGH VD\ VHQGV D PHVVDJH FRQWDLQLQJ
WR DQRWKHU UHSUHVHQ
WKLV ODQGPDUN OLVW
WDWLYH QRGH VD\ RI RQH QHLJKERULQJ UHJLRQ ,I
GRHV QRW
¿QG DQ\ PXWH[ SDLU LQ WKH WZR ODQGPDUN OLVW LW UHSOLHV D SRVLWLYH
WR DOORZ WKH PHUJLQJ RI
DQG
PHVVDJH WR
7KH PHUJLQJ SURFHVV LV VLPSOH EURDGFDVWV D PHVVDJH WR DVN
DOO QRGHV LQ LWV RZQ UHJLRQ WR XSGDWH WKHLU UHJLRQ ,'V WKDW LV
,Q DGGLWLRQ
ZLOO XSGDWH LWV ODQGPDUN OLVW
WR LQFOXGH V ODQGPDUN OLVW 7KLV SURFHVV ZLOO FRQWLQXH XQWLO QR
PRUH QHLJKERULQJ UHJLRQV FDQ EH PHUJHG 7KH UHVXOW RI WKLV VWHS
LV VKRZQ LQ )LJ G ZKHUH HLJKW UHJLRQV DUH ¿QDOO\ JHQHUDWHG
E. Renement
*HQHUDOO\ WKH VHW RI D QHWZRUN
V PXWH[ SDLUV FDQ EH XVHG
WR JHQHUDWH VWULFWO\ FRQYH[ UHJLRQV $V ZH WDUJHW DSSUR[LPDWH
FRQYH[ VHJPHQWDWLRQ ZH FDQ JHQHUDWH VLJQL¿FDQWO\ IHZHU SDU
WLWLRQV E\ LJQRULQJ PXWH[ SDLUV WKDW OHDG WR VPDOO FRQFDYLWLHV
7R GR VR ZH H[SORLW WKH GH¿QLWLRQ RI PXWH[ SDLU LQWUR
GXFHG LQ 6HFWLRQ ,,& %DVHG RQ WKH FRDUVH VHJPHQWDWLRQ UH
VXOW >)LJ G@ WZR UHJLRQV WKDW DUH QRW D PXWH[ SDLU FDQ EH
PHUJHG
7KLV SURFHVV ZRUNV DV IROORZV (DFK UHSUHVHQWDWLYH QRGH
¿UVW ¿QGV DOO PXWH[ SDLUV ZLWK LWV QHLJKERULQJ UHJLRQ :LWKRXW
DQG
DUH D PXWH[
ORVV RI JHQHUDOLW\ ZH DVVXPH
SDLU ,I WKHUH H[LVW WZR FXWV VD\ DQG LQ
VXFK WKDW
DQG
WKH
DQG
GHWHUPLQH ZKHWKHU D PXWH[ SDLU
UHJLRQV
H[LVWV 7KXV WKH WZR FXWV DQG SHUIRUP ÀRRGLQJ ZLWKLQ WKH
UHJLRQV
DQG
VR WKDW WKH UHPDLQLQJ QRGHV KDYH
WKH LQIRUPDWLRQ RI LWV KRS GLVWDQFH WR WKH FXWV
(DFK QRGH ZLWK D ODQGPDUN ,'
WKHQ
FKHFNV LWV KRS GLVWDQFH WR WKH FXW
$ QHJDWLYH PHVVDJH
ZKHQ LWV KRS
LV WKHQ UHSOLHG WR WKH UHSUHVHQWDWLYH QRGH
GLVWDQFH LV JUHDWHU WKDQ ,I ERWK DQG GR QRW UHFHLYH DQ\
QHJDWLYH UHSO\ QR PXWH[ SDLU H[LVWV ,Q WKLV FDVH WKH QRGH QR
WL¿HV WKH QRGH WKDW WKHVH WZR UHJLRQV FDQ EH PHUJHG 7KDW LV
DOO QRGHV LQ WKH UHJLRQ RI
ZLOO XSGDWH WKHLU UHJLRQ ,' WR
7KLV SURFHVV ZLOO FRQWLQXH XQWLO QR PRUH QHLJKERULQJ UH
JLRQV FDQ EH PHUJHG )LJ F VKRZV WKH UH¿QHG UHVXOW 1RWH WKDW
HDFK RI WKH REWDLQHG VXEQHWZRUNV LV DQ
FRQYH[ UHJLRQ
,9 ',6&866,21
A. Time Complexity and Message Complexity
7LPH DQG PHVVDJH FRPSOH[LW\ DUH LPSRUWDQW IDFWRUV IRU DQ
HI¿FLHQW VHJPHQWDWLRQ DOJRULWKP /HW EH WKH WRWDO QXPEHU RI
QRGHV LQ WKH QHWZRUN DQG WKH QXPEHU RI UHJLRQV JHQHUDWHG
E\ WKH &216(/ DOJRULWKP )RU VLPSOLFLW\ ZH DVVXPH WKDW DOO
-,$1* et al. &211(&7,9,7<%$6(' 6(*0(17$7,21 ,1 /$5*(6&$/( '' 6(1625 1(7:25.6
WKH QRGHV DUH URXJKO\ XQLIRUPO\ GLVWULEXWHG RYHU WKH VHQVLQJ
DUHD :H FRQVLGHU WZR FDVHV LQ ' IRU ' WKH SURRI LV TXLWH
VLPLODU ,I WKH VHQVRU DUHD LV OLNH D FLUFOH RU VTXDUH WKH GLDPHWHU
RWKHUZLVH
LV DVVXPHG WR EH
Theorem 1: 7KH WLPH FRPSOH[LW\ RI &216(/ LV
LV WKH QHWZRUN VL]H
ZKHUH
Proof: :H RQO\ SURYH WKLV WKHRUHP LQ D ' VSDFH IRU VLP
SOLFLW\ IRU WKH ' FDVH WKH SURRI LV YHU\ VLPLODU )LUVW WKH
RULJLQ QRGHV RQ WKH QHWZRUN ERXQGDU\ DUH IRXQG YLD JOREDO
ÀRRGLQJ 7KLV VWHS LQWURGXFHV D WLPH FRPSOH[LW\ RI
RU
IRU D QHWZRUN ZLWK D
GLDPHWHU 6HFRQG WR
SHUIRUP
FRQVWUXFW WKH 5HHE JUDSK WKH VHW RI QRGHV RQ
ODQGPDUN VHOHFWLRQ $VVXPLQJ D
GLDPHWHU WKH QXPEHU
RI QRGHV RQ
LV
IRU D
GL
DPHWHU WKH QXPEHU LV
,Q WKLV FDVH WKLV SURFHVV RQ UHVXOWV
RU
IRU D
GLDPHWHU
LQ D WLPH FRPSOH[LW\ RI
VLQFH WKH QRGHV RQO\ IRUZDUG WKH PHVVDJH FRQWDLQLQJ WKH ODUJHVW
QRGH ,' 7KH WRWDO WLPH FRPSOH[LW\ RI FRQVWUXFWLQJ WKH 5HHE
JUDSK LV WKXV
IRU D QHWZRUN ZLWK
D
GLDPHWHU WKH WLPH FRPSOH[LW\ LV
DIWHU DOO ODQGPDUN QRGHV LQIRUP WKHLU ORFDO VLPSOL¿HG
WRSRORJ\ JUDSKV WR WKH RULJLQ QRGHV
7KH VWHS RI FRDUVH VHJPHQWDWLRQ FDQ EH GRQH LQ D GLVWULEXWHG
ZD\²WKH ÀRRGLQJ LV OLPLWHG ZLWKLQ UHJLRQV :H FRQVLGHU WKH
ZRUVW FDVH ZKHUH WKH QXPEHU RI QRGHV LQ HDFK UHJLRQ LV FRPSD
UDEOH WR WKH QXPEHU RI VHQVRU QRGHV LQ WKH ZKROH QHWZRUN 7KDW
QRGHV LQ HDFK UHJLRQV 6LQFH WKLV SURFHVV
LV WKHUH DUH
LV VLPLODU WR WKH ODQGPDUN VHOHFWLRQ LWV WLPH FRPSOH[LW\ LV
>@ 1H[W IRU WKH SURFHGXUH RI PHUJLQJ UHJLRQV VLQFH
WKH QHLJKERULQJ UHSUHVHQWDWLYH QRGHV ZLOO FRPPXQLFDWH ZLWK
HDFK RWKHU WKH WLPH FRPSOH[LW\ LV WKH GLDPHWHU RI UHJLRQV WKDW
RU
IRU D GLDPHWHU
LV
)LQDOO\ LQ WKH VWHS RI UH¿QHPHQW WKH FXWV SHUIRUP ÀRRGLQJ
RU
ZLWKLQ WKH UHJLRQV ZKLFK KDV D WLPH FRPSOH[LW\ RI
IRU WKH ZRUVW FDVH 7KHQ WKH UHSO\ PHVVDJHV WUDYHOLQJ
IURP QRGHV WR WKH UHSUHVHQWDWLYH QRGH OHDG WR D WLPH FRPSOH[LW\
RU
IRU WKH ZRUVW FDVH 2YHUDOO WKH WLPH FRP
RI
SOH[LW\ RI &216(/ LV
Theorem 2: &216(/ KDV D PHVVDJH FRPSOH[LW\ RI
Proof: )RU EUHYLW\ ZH IRFXV RQ WKH ' VSDFH DJDLQ )LUVW
WKH JOREDO ÀRRGLQJ RSHUDWLRQV DUH SHUIRUPHG WR ¿QG WKH RULJLQ
6HFRQG
QRGHV LQWURGXFLQJ D PHVVDJH FRPSOH[LW\ RI
FRQVWUXFWLQJ WKH 5HHE JUDSK UHTXLUHV D SURFHVV VLPLODU WR WKH
ODQGPDUN VHOHFWLRQ 5HFDOO WKDW RQ
WKHUH H[LVW
QRGHV RU
IRU WKH ZRUVW FDVH HDFK RI ZKLFK UDQGRPO\ GH
FODUHV LWVHOI WR EH D ODQGPDUN ZLWK D JLYHQ SUREDELOLW\ )RU VLP
ZKHUH
SOLFLW\ RI DQDO\VLV WKLV SUREDELOLW\ LV VHW WR
LV D FRQVWDQW $V VXFK RQO\
QRGHV SHUIRUP ÀRRGLQJ ZLWKLQ
ZKLFK LQFXUV D IHZ VFRSHG ÀRRGLQJ RSHUDWLRQV $F
LV DW PRVW
FRUGLQJO\ WKH FRVW RI ORFDO ÀRRGLQJ RQ
RU
IRU WKH ZRUVW FDVH 6LQFH WKH GLDPHWHU LV
LH
RU
WKH PHVVDJH FRVW LV
,W LV
WKHUH RQO\ H[LVW
QRWHG WKDW IRU D QHWZRUN ZLWK D GLDPHWHU
QRGHV RQ
,Q WKLV FDVH WKH PHVVDJH FRVW LV VWLOO
7KLUG LQ WKH VWHS RI FRDUVH VHJPHQWDWLRQ WKH ÀRRGLQJ
LV OLPLWHG ZLWKLQ UHJLRQV QRW RYHU WKH ZKROH QHWZRUN UHVXOWLQJ
)LQDOO\ GXULQJ WKH UH¿QH
LQ D PHVVDJH FRPSOH[LW\ RI
PHQW WKH FXWV SHUIRUP ÀRRGLQJ ZLWKLQ WKH UHJLRQV ZKLFK DOVR
2YHUDOO WKH PHV
LQWURGXFHV D PHVVDJH FRPSOH[LW\ RI
VDJH FRPSOH[LW\ RI &216(/ LV
)LJ ([DPSOH ' QHWZRUN ZLWK DQ LQWHUQDO KROH ZLWK QRGHV DQG DY
HUDJH GHJUHH LV &216(/ JHQHUDWHV FRQYH[ UHJLRQV ZKHUH WKH SRRU
YLVXDOL]DWLRQ LV GXH WR WKH GLVSOD\ OLPLWDWLRQ RI ' REMHFWV D 2ULJLQDO QHW
ZRUN E 6HJPHQWDWLRQ UHVXOW
)LJ 9HU\ VSDUVH VHQVRU QHWZRUN GHSOR\HG LQ DQ /VKDSH DUHD
7KHRUHP LPSOLHV WKDW ZKLOH RXU DOJRULWKP DOZD\V XVHV
ÀRRGLQJ RSHUDWLRQV WR FROOHFW QHFHVVDU\ LQIRUPDWLRQ LQ HDFK
VWHS WKH FRPPXQLFDWLRQ FRVW ZLOO QRW LQFUHDVH WRR PXFK VLQFH
ZH OLPLW WKH ÀRRGLQJ ZLWKLQ ORFDO DUHDV DV PXFK DV SRVVLEOH
B. Special Cases for Segmentation
:KLOH WKH VHJPHQWDWLRQ DOJRULWKP UHTXLUHV QR ERXQGDU\ LQ
IRUPDWLRQ LQ PRVW FDVHV LQ VRPH ' FDVHV URXJK QHWZRUN
ERXQGDULHV PD\ KDYH WR EH NQRZQ ZKHQ LQWHUQDO KROHV H[LVW
)LJ VKRZV DQ H[DPSOH ZKHUH WKHUH H[LVW WZR ERXQGDU\ VXU
IDFHV ZLWK DQ LQWHUQDO KROH LQ D ' QHWZRUN
,W FDQ EH VHHQ WKDW ZKHQ WKH ÀRRGHG PHVVDJH IURP WKH RULJLQ
QRGH UHDFKHV D QHZ ERXQGDU\ VXUIDFH D QHZ YHUWH[ VKRXOG EH
JHQHUDWHG LQ WKH 5HHE JUDSK 7R DFKLHYH URXJK ERXQGDU\ LGHQ
WL¿FDWLRQ H[LVWLQJ VROXWLRQV VXFK DV WKH RQH LQ >@ FDQ EH XVHG
$V D UHVXOW HDFK ERXQGDU\ VXUIDFH LV DVVLJQHG D VXUIDFH ,' 7R
FRQVWUXFW WKH 5HHE JUDSK QHZ YHUWLFHV DUH LQVHUWHG ZKHQ D QHZ
ERXQGDU\ VXUIDFH LV PHW GXULQJ WKH RULJLQV
ÀRRGLQJ SURFHVV
7KH UHVW RI WKH VWHSV DUH VLPLODU DQG WKXV FRDUVH VHJPHQWDWLRQ
FDQ VWLOO EH JHQHUDWHG IROORZHG E\ WKH PHUJLQJ DQG UH¿QHPHQW
VWHSV 7KH UHVXOW LV VKRZQ LQ )LJ E
C. Node Density Requirement of CONSEL
&216(/ RQO\ UHTXLUHV D QHWZRUN WR EH FRQQHFWHG VR LQ SULQ
FLSOH LW ZRUNV FRUUHFWO\ IRU ERWK GHQVH DQG VSDUVH QHWZRUNV
*HQHUDOO\ WKH GHQVHU WKH QHWZRUN QRGHV WKH EHWWHU WKH VHJPHQ
WDWLRQ SHUIRUPDQFH )RU D YHU\ VSDUVH QHWZRUN KRZHYHU WKH
DOJRULWKP PD\ SURGXFH PDQ\ VPDOO DQG OHVV PHDQLQJIXO VHJ
PHQWV 7KLV LV EHFDXVH LQ WKLV FDVH WKH FRQQHFWLYLW\ RI WKH QHW
ZRUN QRGHV FDQQRW ZHOO UHSUHVHQW WKH JHRPHWULF VKDSH RI WKH
QHWZRUN )LJ VKRZV DQ H[DPSOH RI D VHQVRU QHWZRUN GHSOR\HG
,((($&0 75$16$&7,216 21 1(7:25.,1* 92/ 12 )(%58$5< )LJ ' SHUIRUPDQFH RI &216(/ D ' VKDSH QRGHV DYJ GHJ
E &KLFDJR DLUSRUW WHUPLQDO VKDSH QRGHV DYJ GHJ F '
VSLUDO VKDSH QRGHV DYJ GHJ G ' ULQJEDOO VKDSH QRGHV
DYJ GHJ H ' VLQJOHKROH VKDSH QRGHV DYJ GHJ I '
6 VKDSH QRGHV DYJ GHJ J ' KHDGVHW VKDSH DYJ GHJ
K ' FURVVULQJ VKDSH DYJ GHJ L ' IRRWSULQW VKDSH
DYJ GHJ )LJ &RPSDULVRQV RQ ' QHWZRUNV &ROXPQV IURP OHIW WR ULJKW UHVXOWV
XVLQJ &216(/ UHVXOWV RI >@ DQG UHVXOWV RI WKH &219(; DOJRULWKP >@
5RZV 6PLOH VKDSH QRGHV DYJ GHJ VLQJOHKROH VKDSH
QRGHV DYJ GHJ &DFWXV VKDSH QRGHV DYJ GHJ $LUSODQH VKDSH DYJ GHJ 6WDU VKDSH DYJ GHJ LQ DQ /VKDSHG DUHD 'XH WR WKH VSDUVH QRGHV DQG OLQNV WKH QHW
ZRUN GRHV QRW TXLWH H[KLELW DQ / VKDSH 7KH PDLQ GLI¿FXOW\ IRU
&216(/ DULVHV IURP WKH IDFW WKDW WKH QHWZRUN
V FRQQHFWLRQV
PD\ QRW GHWHUPLQH D GHWHUPLQLVWLF VKDSH RI WKH QHWZRUN ,Q RWKHU
ZRUGV JLYHQ YHU\ OLPLWHG FRQQHFWLRQ LQIRUPDWLRQ &216(/
FDQQRW SUHFLVHO\ LQIHU WKH VKDSH RI WKH QHWZRUN GXH WR WKH ODFN RI
VXI¿FLHQW FRQVWUDLQWV RQ WKH QRGHV
SRVLWLRQV 7KH UHDVRQ EHKLQG
WKLV LV H[SODLQHG E\ WKH WKHRU\ RI ULJLG JUDSKV >@ ZKLFK VWXGLHV
WKH FRQGLWLRQV IRU D JUDSK WR KDYH D XQLTXH HPEHGGLQJ RQWR WKH
SODQH %HFDXVH RI WKLV WKHRUHWLFDO UHVWULFWLRQ WKHUH H[LVWV QR VHJ
PHQWDWLRQ DOJRULWKP WKDW ZRUNV ZHOO IRU FDVHV OLNH WKLV 7KHUH
IRUH WKH FRQVHTXHQFH RI RYHUVHJPHQWDWLRQ PXVW EH WDNHQ LQWR
DFFRXQW EHIRUH RQH FKRRVHV DQ\ FRQQHFWLYLW\EDVHG DOJRULWKPV
LQFOXGLQJ &216(/ IRU D YHU\ VSDUVH QHWZRUN ZKRVH VKDSH LV
KDUG WR GH¿QH JHRPHWULFDOO\
9 6,08/$7,216
:H KDYH FRQGXFWHG D VHULHV RI VLPXODWLRQV H[SHULPHQWV RQ
YDULRXV QHWZRUN WRSRORJLHV WR FRPSDUH &216(/ ZLWK WKH DO
JRULWKPV LQ >@ DQG >@ :H HYDOXDWH KRZ WKH SHUIRUPDQFH
RI &216(/ LV DIIHFWHG E\ IDFWRUV VXFK DV QRGH GHQVLW\ UDGLR
PRGHO QRGH GLVWULEXWLRQ HWF 7KH GHIDXOW VHWWLQJV DUH DV IRO
ORZV 6HQVRUV DUH GHSOR\HG ZLWK D SHUWXUEHG JULG PRGHO ZKHUH
WKH JULG KDV D ZLGWK DURXQG DQG WKH UDGLR UDQJH LV DURXQG
7KH QHWZRUNV KDYH DQ DYHUDJH QRGH GHJUHH RI DURXQG IRU ' DQG IRU ' :H VHW WKH SDUDPHWHU WR EH KRSV DQG
WR EH KRSV
A. Evaluation on 2-D Networks
:H ¿UVW FRPSDUH &216(/ WR WZR VWDWHRIWKHDUW DOJRULWKPV
LQ >@ DQG >@ GHVLJQHG IRU ' QHWZRUNV )LJ VKRZV WKH UH
VXOWV 6LQFH WKHVH DOJRULWKPV UHO\ RQ WKH NQRZOHGJH RI QHWZRUN
ERXQGDULHV LW FDQ EH VHHQ WKDW WKH\ SURGXFH VLJQL¿FDQWO\ PRUH
UHJLRQV $OVR WKH UHVXOWV E\ >@ DQG >@ DUH TXLWH VHQVLWLYH WR
ERXQGDU\ QRLVH RU ERXQGDU\ GHIRUPDWLRQ DV ZH H[SODLQHG LQ
6HFWLRQ , ,Q FRQWUDVW &216(/ SURYLGHV D ERXQG RI FRQYH[LW\
GHYLDWLRQ RI UHJLRQV UHVXOWLQJ LQ DSSURSULDWH VHJPHQWDWLRQ UH
VXOWV VPDOOHU QXPEHU RI VHJPHQWDWLRQ UHJLRQV
B. Evaluation on 3-D Networks
)LJ VKRZV WKH VHJPHQWDWLRQ UHVXOWV RI &216(/ IRU VHY
HUDO ' QHWZRUNV :H GR QRW LQFOXGH D FRPSDULVRQ WR WKH RQO\
SUHYLRXV DOJRULWKP ZLWK OLPLWHG ' VHJPHQWDWLRQ FDSDELOLW\
LQ >@ EHFDXVH LWV UHOLDQFH RQ ERWWOHQHFN LGHQWL¿FDWLRQ SUH
YHQWV LW IURP ZRUNLQJ IRU PRVW QHWZRUNV LQ )LJ H[FHSW
IRU )LJ G :H FDQ VHH WKDW &216(/ ZRUNV ZHOO IRU '
-,$1* et al. &211(&7,9,7<%$6(' 6(*0(17$7,21 ,1 /$5*(6&$/( '' 6(1625 1(7:25.6
)LJ 6HJPHQWDWLRQ UHVXOWV ZLWK YDU\LQJ QRGH GHQVLWLHV D QRGHV DYJ
GHJJ E QRGHV DYJ GHJ F QRGHV DYJ GHJ G QRGHV DYJ GHJ H QRGHV DYJ GHJ I QRGHV
DYJ GHJ )LJ 6HJPHQWDWLRQ UHVXOWV XQGHU WKH 4XDVL8'*8%* UDGLR PRGHO
E
F
G
H
I
D
QHWZRUNV DOZD\V \LHOGLQJ SURSHU VHJPHQWDWLRQ UHVXOWV )RU H[
DPSOH LQ WKH VKDSH QHWZRUN VL[ FRQYH[ UHJLRQV DUH JHQHUDWHG
UHÀHFWLQJ WKH LPSDFW RI WKH WZR KROHV LQ WKH QHWZRUN WRSRORJ\
C. Sensitivity to Node Density
)LJ VKRZV WKH UHVXOWV RI QHWZRUNV ZLWK D YDULHW\ RI QRGH
GHQVLWLHV 7KHRUHWLFDOO\ WKH KLJKHU WKH QRGH GHQVLW\ WKH FORVHU
WKH QHWZRUN WR D FRQWLQXRXV GRPDLQ 7KLV PHDQV WKDW KRS FRXQW
VHUYHV DV D JRRG DSSUR[LPDWLRQ RI (XFOLGLDQ GLVWDQFH )LUVW
WKH HGJH EHWZHHQ WZR UHJLRQV LV VPRRWKHU FORVHU WR D VWUDLJKW
OLQH ZKHQ WKH QRGH GHQVLW\ LV KLJKHU 6HFRQG ZH REVHUYH LQ
)LJ G DQ LQFUHDVHG QXPEHU RI UHJLRQV 7KH UHDVRQ LV WKDW
ZKHQ WKH DYHUDJH GHJUHH LV WRR ORZ VPDOOHU UHJLRQV RI IHZ
VHQVRU QRGHV FDQ EH SURGXFHG GXH WR WKH YDULDWLRQ RI QRGH
FRQQHFWLYLW\
)LJ 6HJPHQWDWLRQ UHVXOWV XQGHU WKH ORJQRUPDO UDGLR PRGHO D
F
G
H
I
E
D. Sensitivity to Radio Model
:H UXQ VLPXODWLRQV XQGHU D GLIIHUHQW UDGLR PRGHO
4XDVL8'* 4XDVL8%* IRU ' QHWZRUNV UDGLR PRGHO ZLWK
D SDUDPHWHU 7KHUH H[LVWV D OLQN EHWZHHQ WZR QRGHV LI WKH
ZKHUH LV WKH FRP
(XFOLGLDQ GLVWDQFH LV OHVV WKDQ
PXQLFDWLRQ UDQJH ,I WKH GLVWDQFH LV EHWZHHQ DQG
WKH OLQN H[LVWV ZLWK D SUREDELOLW\ RI
1R OLQN H[LVWV
:H YDU\ WKH
ZKHQ WKH GLVWDQFH LV JUHDWHU WKDQ
YDOXH ZKLOH DGMXVWLQJ WR PDNH WKH DYHUDJH QRGH GHJUHH LQ WKH
QHWZRUNV QHDUO\ WKH VDPH
:H VKRZ WKH VHJPHQWDWLRQ UHVXOWV XQGHU WKH 4XDVL
8'%8%* PRGHO E\ YDU\LQJ WKH YDOXHV LQ )LJ :H FDQ
REVHUYH GHJUDGHG SHUIRUPDQFH RI FXWV VKDUHG HGJHVVXUIDFHV
EHWZHHQ WZR UHJLRQV XQGHU WKLV PRGHO 1RQHWKHOHVV WKH
QHWZRUN LV VWLOO SDUWLWLRQHG LQWR VHYHUDO DSSUR[LPDWHO\ FRQYH[
UHJLRQV E\ &216(/
$ VHFRQG UDGLR PRGHO WKDW ZH H[DPLQH LV WKH ORJQRUPDO
PRGHO )RU WZR QRGHV DQG WKH SUREDELOLW\ RI D OLQN H[
LVWLQJ EHWZHHQ WKHP LV EDVHG RQ D ORJQRUPDO VKDGRZLQJ UDGLR
PRGHO >@
ZKHUH
LV WKH QRUPDOL]HG GLVWDQFH EHWZHHQ QRGHV DQG
LV D FRQVWDQW LV WKH VWDQGDUG GHYLDWLRQ
RI VKDGRZLQJ DQG LV WKH SDWKOHVV H[SRQHQW (PSLULFDOO\
PD\ YDU\ EHWZHHQ DQG >@ $Q LPSRUWDQW IHDWXUH RI WKH ORJ
QRUPDO UDGLR PRGHO LV WKDW WKH OLQN EHWZHHQ WZR QRGHV ZKRVH
QRUPDOL]HG GLVWDQFH LV OHVV WKDQ PD\ QRW H[LVW DQG WKH OLQN
EHWZHHQ QRGHV ZKRVH QRUPDOL]HG GLVWDQFH LV ODUJHU WKDQ H[LVWV
ZLWK D QRQ]HUR SUREDELOLW\
)LJ VKRZV WKH VHJPHQWDWLRQ UHVXOWV IRU YDULRXV YDOXHV
:H REVHUYH GHJUDGHG SHUIRUPDQFH ZLWK D ODUJHU 7KH UHDVRQ
LV VLPLODU $ QRGH PD\ ¿QG D QHLJKERU IDU DZD\ IURP LWVHOI
0RUH VHYHUHO\ ZKHQ LV ODUJH VD\
LQ )LJ I RQO\
IRXU UHJLRQV DUH JHQHUDWHG ¿QDOO\ :H FRQFOXGH WKDW &216(/
DOJRULWKP ZRUNV EHVW IRU D PRGHUDWH YDOXH RI VD\
LQ
WKH ORJQRUPDO UDGLR PRGHO
7KH WKLUG UDGLR PRGHO XVHG LQ RXU VLPXODWLRQ LV WKH SURED
ELOLVWLF FRQQHFWLYLW\ PRGHO ZKHUH ZH VWDUW ZLWK WKH XQLW GLVN
JUDSK PRGHO DQG UHPRYH HDFK HGJH ZLWK SUREDELOLW\
$V FDQ EH VHHQ IURP )LJ &216(/ FDQ JHQHUDWH DSSUR
SULDWH VHJPHQWDWLRQ UHVXOWV UHÀHFWLQJ LWV UREXVWQHVV WR WKLV UDGLR
PRGHO
,((($&0 75$16$&7,216 21 1(7:25.,1* 92/ 12 )(%58$5< )LJ D QRGHV DYJ GHJ E QRGHV DYJ GHJ F QRGHV DYJ GHJ )LJ 6HJPHQWDWLRQ UHVXOWV XQGHU WKH SUREDELOLVWLF FRQQHFWLYLW\ PRGHO D
E
F
G
H
I
)LJ D QRGHV DYJ GHJ E QRGHV DYJ GHJ F QRGHV DYJ GHJ E. Sensitivity to Node Distribution
:H QH[W FRQVLGHU DQRWKHU VHQVRU SODFHPHQW VFKHPH XQL
IRUP UDQGRP GLVWULEXWLRQ 7KLV GLVWULEXWLRQ FRPSDUHG WR WKH
SHUWXUEHG JULG PRGHO JHQHUDWHV PRUH UDQGRPQHVV LQ QRGH
GHSOR\PHQW :H VKRZ WKH UHVXOWV LQ )LJ :LWK WKH LQFUHDVHG
UDQGRPQHVV WKH VHJPHQWDWLRQ UHVXOWV VKRZ QR VLJQL¿FDQW
GLIIHUHQFH FRPSDUHG WR WKHLU FRXQWHUSDUWV LQ )LJV DQG 'H
VSLWH WKH KLJKHU YDULDELOLW\ RI WKH QRGH GLVWULEXWLRQ &216(/
SDUWLWLRQV WKH QHWZRUN DFFRUGLQJ WR WKH 5HHE JUDSK DQG PXWH[
SDLUV ZKLFK PDNHV LWVHOI UREXVW WR WKH YDULDWLRQ RI QRGH
FRQQHFWLYLW\
:H QH[W H[DPLQH &216(/ XQGHU D QRQXQLIRUP QRGH GLVWUL
EXWLRQ )LJ VKRZV WKH UHVXOWV RI &216(/ ZKHUH RI DOO
QRGHV DUH GLVWULEXWHG LQ WKH ULJKW KDOI RI WKH VHQVRU DUHD 7KLV
QRQXQLIRUP GLVWULEXWLRQ OHDGV WR PRUH YDULDEOH QRGH FRQQHF
WLYLW\ 1RQHWKHOHVV WKHUH LV QR VLJQL¿FDQW GLIIHUHQFH FRPSDUHG
WR WKH UHVXOWV IURP WKH SUHYLRXV H[SHULPHQWV 7KH UHDVRQ LV WKDW
WKH 0RUVH IXQFWLRQ XVHG LQ &216(/ XWLOL]HV QR QHLJKERUKRRG
GHQVLW\ LQIRUPDWLRQ
)LJ 6HJPHQWDWLRQ UHVXOWV ZLWK YDU\LQJ YDOXHV 7KH ¿UVW URZ VKRZV D
QHWZRUN ZLWK PDQ\ VPDOO ERXQGDU\ GHIRUPDWLRQV ,W FRQWDLQV VHQVRU QRGHV
E
F
G
DQG LWV DYHUDJH GHJUHH LV D
I
H
7$%/( ,
0(66$*( &267 2) &216(/ )25 9$5,286 1(7:25.6
F. Sensitivity to the Parameter
5HFDOO WKDW DQG FDQ EH FRQVLGHUHG DV WZR SDUDPHWHUV
DOORZLQJ WKH DOJRULWKP WR FRQWURO WKH OHYHO RI FRQYH[LW\ RI
JHQHUDWHG UHJLRQV 6LQFH WKH\ KDYH VLPLODU LQÀXHQFH RQ WKH
FRQYH[LW\ GHYLDWLRQ ZH VWXG\ WKH DOJRULWKP
V VHQVLWLYLW\ WR
WKH SDUDPHWHU )LJ GHSLFWV WKH VHJPHQWDWLRQ UHVXOWV
ZLWK YDU\LQJ
YDOXHV ,W LV IRXQG WKDW ZLWK DQ LQFUHDVHG
YDOXH PRUH DQG PRUH DSSUR[LPDWHO\ FRQYH[ UHJLRQV DUH
JURXSHG WRJHWKHU 5HFDOO WKDW HDFK RI WKH REWDLQHG UHJLRQV
LV DQ
FRQYH[ UHJLRQ 7KLV SDUDPHWHU DOVR SURYLGHV D
ÀH[LEOH WRRO WR EDODQFH WKH QXPEHU RI JHQHUDWHG UHJLRQV DQG
WKHLU FRQYH[LW\
G. Message Cost
:H QH[W HYDOXDWH WKH PHVVDJH FRVW RI &216(/ IRU GLIIHUHQW
QHWZRUNV PHDVXUHG E\ WKH WRWDO QXPEHU RI WUDQVPLWWHG PHV
VDJHV VHH 7DEOH , ,Q WKLV WDEOH WKH SURFHGXUHV RI HVWDEOLVKLQJ
-,$1* et al. &211(&7,9,7<%$6(' 6(*0(17$7,21 ,1 /$5*(6&$/( '' 6(1625 1(7:25.6
WKH 0RUVH IXQFWLRQV DQG FRQVWUXFWLQJ WKH 5HHE *UDSK DUH
ODEHOHG ³6WHS ´ ZKRVH PHVVDJH FRVW DULVHV IURP WKH JOREDO
ÀRRGLQJ IURP WKH RULJLQ QRGHV $OVR WKH UHPDLQLQJ SURFH
GXUHV RI &216(/ DUH ODEHOHG ³6WHS ´ ZKRVH PHVVDJH FRVW LV
FDXVHG E\ WKH RSHUDWLRQV RI JURXSLQJ VHQVRU QRGHV :H PDNH
VHYHUDO REVHUYDWLRQV )LUVW WKH FRVW RI 6WHS GRPLQDWHV WKH
FRVW 7KDW LV WKH ÀRRGLQJ RSHUDWLRQV LQLWLDWHG E\ WKH RULJLQ
QRGHV DFFRXQW IRU WKH PDMRULW\ RI WUDI¿F E\ &216(/ 7KH
UHDVRQ LV WKDW WKLV VWHS QRW RQO\ LQYROYHV JOREDO QHWZRUNZLGH
ÀRRGLQJ RSHUDWLRQV EXW DOVR UHTXLUHV PDQ\ ORFDO ÀRRGLQJ
RSHUDWLRQV WKDW KDYH WR EH GRQH IRU HYHU\ VHW RI
7KHVH
DUH QHHGHG WR ¿QG GRPLQDWLQJ ODQGPDUN QRGHV LQ RUGHU WR ¿JXUH
RXW WKH ORFDO VLPSOL¿HG QHWZRUN WRSRORJ\ DQG WR ERXQG WKH
OHYHO RI FRQFDYLW\ 6HFRQG &216(/ LV VFDODEOH LQ WHUPV RI
PHVVDJH FRVW FRQ¿UPLQJ WKH WKHRUHWLFDO UHVXOW LQ 7KHRUHP 7DNH URZV ± LQ 7DEOH , DV DQ H[DPSOH :LWK LQFUHDVHG QHW
ZRUN VL]H WKH WUDI¿F FRVW LV LQFUHDVHG URXJKO\ LQ SURSRUWLRQ WR
WKH QHWZRUN VL]H 7KLV OLQHDU WUHQG PDNHV &216(/ SRWHQWLDOO\
DSSOLFDEOH WR D ZLGH UDQJH RI VFHQDULRV LQ SUDFWLFH 7KLUG
ZH FDQQRW VHH VLJQL¿FDQW GLIIHUHQFH RI FRVW EHWZHHQ ' DQG
' QHWZRUNV :H FRQFOXGH WKDW WKH PHVVDJH FRPSOH[LW\ RI
&216(/ LV QRW FRUUHODWHG WR WKH GLPHQVLRQ EXW UDWKHU GHSHQGV
RQ WKH QHWZRUN VL]H
9, $33/,&$7,216
1HWZRUN VHJPHQWDWLRQ HQDEOHV WUDGLWLRQDO DOJRULWKPV RUL
HQWHG WR VLPSOH QHWZRUN JHRPHWU\ WR UXQ HI¿FLHQWO\ IRU FRPSOH[
DQG LUUHJXODU HQYLURQPHQWV ,Q WKLV VHFWLRQ ZH VWXG\ KRZ LW
EHQH¿WV WZR LPSRUWDQW DSSOLFDWLRQV JHRJUDSKLF URXWLQJ DQG
FRQQHFWLYLW\EDVHG ORFDOL]DWLRQ
A. Geographic Routing
*HRJUDSKLF URXWLQJ LV D URXWLQJ SDUDGLJP LQ ZKLFK D VHQVRU
QRGH JUHHGLO\ IRUZDUGV SDFNHWV WR LWV QHLJKERU FORVHVW WR WKH
GHVWLQDWLRQ ,W ZRUNV ZHOO ZKHQ WKH VKDSH RI D VHQVRU ¿HOG LV
DSSUR[LPDWHO\ FRQYH[ ZKHUH WKH VRXJKW URXWH VKRXOG DSSUR[
LPDWHO\ IROORZ D VWUDLJKW OLQH 7KLV DVVXPSWLRQ KRZHYHU GRHV
QRW KROG IRU JHRPHWULFDOO\ FRPSOH[ HQYLURQPHQWV ,Q WKH SUHV
HQFH RI KROHV RU FRQFDYH FRUQHUV WKH VWUDLJKWOLQH FRXUVH RI
JUHHG\ IRUZDUGLQJ FDQ EH VHULRXVO\ GLVUXSWHG OHDGLQJ WR YHU\
SRRU SHUIRUPDQFH >@ >@
:LWK QHWZRUN VHJPHQWDWLRQ ZH FDQ FLUFXPYHQW WKH DERYH
SUREOHP E\ UXQQLQJ JHRJUDSKLF URXWLQJ ZLWKLQ HDFK UHJLRQ
$IWHU WKH VHJPHQWDWLRQ HDFK QRGH REWDLQV D XQLTXH UHJLRQDO
,' DQG NQRZV WKH ,' RI LWV 5HHE FRPSRQHQW ODQGPDUN QRGH RU
LWV 5HHE ODQGPDUN ,Q DGGLWLRQ LQ HDFK UHJLRQ XVLQJ H[LVWLQJ
FRRUGLQDWH DVVLJQPHQW DOJRULWKPV VXFK DV >@ DQG >@ ZH
FDQ DVVLJQ D VHW RI YLUWXDO FRRUGLQDWHV WR HDFK QRGH $W WKH
VDPH WLPH WKH 5HHE FRPSRQHQW ODQGPDUN QRGHV FDQ KHOS ZLWK
LQWHUUHJLRQ URXWLQJ 7R WKDW HQG HDFK 5HHE ODQGPDUN ÀRRGV
WKH JOREDO QHWZRUN WR HVWDEOLVK D VKRUWHVW SDWK WUHH DOORZLQJ
HYHU\ RWKHU QRGH LQ WKH QHWZRUN WR UHDFK LW YLD VKRUWHVW SDWK
7KH VHJPHQWDWLRQDVVLVWHG JHRJUDSKLF URXWLQJ LV VLPSOH :KHQ
D SDFNHW LV UHTXHVWHG WR URXWH IURP D VRXUFH QRGH WR D GHVWLQD
LV ¿UVW JUHHGLO\ URXWHG WR V 5HHE ODQGPDUN XVLQJ
WLRQ QRGH
WKH YLUWXDO FRRUGLQDWHV 7KHQ WKH SDFNHW LV URXWHG WR V 5HHE
ODQGPDUN YLD VKRUWHVW SDWK )LQDOO\ WKH SDFNHW LV URXWHG WR DJDLQ XVLQJ JUHHG\ IRUZDUGLQJ EDVHG RQ WKH YLUWXDO FRRUGLQDWHV
)LJ D 5RXWLQJ VXFFHVVIXO UDWH DQG E WUDQVPLVVLRQ VWUHWFK
:H FDUU\ RXW VLPXODWLRQV RQ YDULRXV QHWZRUNV DQG WKH UHVXOWV
RI URXWLQJ VXFFHVVIXO UDWH DQG WUDQVPLVVLRQ VWUHWFK DUH VKRZQ LQ
)LJ :H DOVR LPSOHPHQW WKH DOJRULWKP LQ >@ DQG LWV VHJ
PHQWDWLRQ UHVXOWV DUH ODEHOHG ³&RQYH[ SDUWLWLRQ´ RU &219(;
IRU VKRUW )LUVW LQ PRVW FDVHV GLUHFW JUHHG\ URXWLQJ ZLWKRXW
VHJPHQWDWLRQ ODEHOHG ³3K\VLFDO ORFDWLRQ´ KDV D URXWLQJ VXF
FHVVIXO UDWH EHORZ :LWK VHJPHQWDWLRQ WKH VXFFHVVIXO
UDWH LV VLJQL¿FDQWO\ KLJKHU FRPLQJ FORVH WR 6HFRQG
)LJ E VKRZV WKH UHVXOWV RI WUDQVPLVVLRQ VWUHWFK GH¿QHG
DV WKH UDWLR RI WKH URXWLQJ SDWK OHQJWK WR WKH VKRUWHVWSDWK KRS
FRXQW EHWZHHQ WKH QRGHV 7KH &216(/ SURWRFRO RXWSHUIRUPV
&219(; UHVXOWLQJ LQ D ± LPSURYHPHQW 7KH UHDVRQ
LV WKDW IRU ' QHWZRUNV &216(/ JHQHUDWHV IHZHU UHJLRQV
FRPSDUHG WR &219(; SRWHQWLDOO\ OHDGLQJ WR D VKRUWHU URXWLQJ
SDWK 7KLUG IRU ' QHWZRUNV FOHDUO\ WKH UHVXOWV ZLWK &216(/
VHJPHQWDWLRQ LV PXFK EHWWHU WKDQ WKDW ZLWKRXW VHJPHQWDWLRQ
ZLWK D SHUIRUPDQFH LPSURYHPHQW LQ VXFFHVVIXO UDWLR
)LQDOO\ IRU '' QHWZRUNV WKH VWUHWFK RI JUHHG\ URXWLQJ
ZLWK &216(/ VHJPHQWDWLRQ LV RQO\ DURXQG 7KDW LV WKH
WUDGLWLRQDO DOJRULWKP²JUHHG\ URXWLQJ GHVLJQHG IRU D VLPSOH
QHWZRUN VKDSH²LV VXFFHVVIXOO\ DGDSWHG WR FRPSOH[ ''
HQYLURQPHQWV ZLWK WKH KHOS RI &216(/
B. Connectivity-Based Localization
/RFDOL]DWLRQ LV FUXFLDO IRU PDQ\ DSSOLFDWLRQV VXFK DV SR
VLWLRQDZDUH GDWD GLVVHPLQDWLRQ DQG SURFHVVLQJ &RQQHFWLYLW\
EDVHG ORFDOL]DWLRQ DLPV WR SURGXFH D UHODWLYH FRRUGLQDWH V\VWHP
IRU D QHWZRUN ZLWKRXW XVLQJ UDQJLQJ WHFKQLTXHV IRU PHDVXULQJ
SK\VLFDO GLVWDQFH EHWZHHQ QRGHV ,Q WKLV DSSURDFK WKH SK\V
LFDO GLVWDQFH EHWZHHQ QRGHV LV HVWLPDWHG ZLWK WKH KRS FRXQW RI
WKHLU VKRUWHVW SDWK UHO\LQJ RQ WKH DVVXPSWLRQ WKDW WKH KRS GLV
WDQFH FRUUHODWHV ZHOO ZLWK (XFOLGHDQ GLVWDQFH +RZHYHU ZKHQ
WKH QHWZRUN WRSRORJ\ LV LUUHJXODU WKH VKRUWHVW SDWK PD\ EH VLJ
QL¿FDQWO\ EHQW $V D UHVXOW WKH KRS GLVWDQFH EHWZHHQ WZR QRGHV
PD\ GHYLDWH YDVWO\ IURP WKH (XFOLGHDQ GLVWDQFH
:LWK VKDSH VHJPHQWDWLRQ ZH RQO\ QHHG WR DSSO\ D WUDGLWLRQDO
ORFDOL]DWLRQ DOJRULWKP WR LQGLYLGXDO UHJLRQV WKHUHE\ DYRLGLQJ
WKH DERYH SUREOHP 7KH VHJPHQWDWLRQDVVLVWHG ORFDOL]DWLRQ DO
JRULWKP LV D VLPSOH H[WHQVLRQ RI H[LVWLQJ DOJRULWKPV )LUVW WKH
QHWZRUN LV VHJPHQWHG LQWR D VHW RI UHJLRQV 6HFRQG ZLWKLQ HDFK
UHJLRQ D WUDGLWLRQDO PXOWLODWHUDLRQ DOJRULWKP VXFK DV WKH DWRPLF
WULODWHUDWLRQ PHWKRG LQ >@ LV DSSOLHG 7KH DOJRULWKP FRPSXWHV
D QRGH
V FRRUGLQDWHV XVLQJ GLVWDQFH PHDVXUHPHQWV WR WKUHHIRXU
UHIHUHQFH SRLQWV 7KLUG ZH FRPELQH WKH FRRUGLQDWHV RI DOO WKH
UHJLRQV LQWR D JOREDO PDS ,Q WKLV VWHS IRU HYHU\ SDLU RI DGMDFHQW
UHJLRQV WKHUH DUH VRPH QRGHV ORFDWHG RQ WKHLU VKDUHG VHJPHQW
OLQHV DQG WKHVH QRGHV DUH DVVLJQHG WZR YLUWXDO FRRUGLQDWHV :H
,((($&0 75$16$&7,216 21 1(7:25.,1* 92/ 12 )(%58$5< ZLWK WKH &216(/ VHJPHQWDWLRQ FRPSDUHG WR WKH &219(;
VFKHPH EHFDXVH &216(/ JHQHUDWHV IHZHU FRQYH[ UHJLRQV
WKHUHE\ DYRLGLQJ WKH HUURU SURSDJDWLRQ LQ &219(; 6HFRQG
WKH DFFXUDF\ RI SXUH PXOWLODWHUDLRQ LV WRR SRRU WR EH DFFHSWDEOH
IRU FRPSOH[ QHWZRUNV FRQWDLQLQJ KROHV RU FRQFDYH UHJLRQV
7KLUG IRU WKH ' QHWZRUN DQ XS WR LPSURYHPHQW LQ
ORFDOL]DWLRQ DFFXUDF\ FDQ EH DWWDLQHG XVLQJ RXU VFKHPH FRP
SDUHG ZLWK &$7/ >@ 7KH UHDVRQ LV WKDW &$7/ VXIIHUV IURP
WKH ORFDWLRQ HVWLPDWLRQ IURP D ORQJ GLVWDQFH ZKHQ WKH QRGH
LV IDU DZD\ IURP WKH DQFKRUV 0RUH VSHFL¿FDOO\ DIWHU HDFK
LWHUDWLRQ QHZO\ ORFDOL]HG QRGHV ZLOO VHUYH DV EHDFRQ QRGHV
DQG ÀRRG WKHLU ORFDWLRQV WKURXJK WKH QHWZRUN 7KH ORFDOL]DWLRQ
HUURUV DIWHU HDFK URXQG ZLOO EH DFFXPXODWHG ,Q DGGLWLRQ WKH
SHUIRUPDQFH RI &$7/ KLJKO\ GHSHQGV RQ WKH FKRLFH RI EHDFRQ
QRGHV ,Q FRQWUDVW WKH WUDGLWLRQDO ORFDOL]DWLRQ DOJRULWKP DSSOLHG
ZLWKLQ HDFK UHJLRQ DYRLGV WKLV SUREOHP 2YHUDOO WKH VHJPHQWD
WLRQDVVLVWHG ORFDOL]DWLRQ FDQ UHFRYHU WKH QHWZRUN OD\RXW ZLWK
VPDOO HUURUV
9,, &21&/86,21
)LJ /RFDOL]DWLRQ UHVXOWV &ROXPQV IURP OHIW WR ULJKW '' ORFDOL]D
WLRQ UHVXOWV ZLWK &216(/ ' ORFDOL]DWLRQ UHVXOWV ZLWK WKH &219(; >@
DOJRULWKP ' ORFDOL]DWLRQ UHVXOWV XVLQJ &$7/ >@ '' ORFDOL]DWLRQ
UHVXOWV XVLQJ SXUH PXOWLODWHUDLRQ ZLWKRXW VHJPHQWDWLRQ 5RZV 6LQJOHKROH
VKDSH &DFWXV VKDSH &KLFDJR DLUSRUW WHUPLQDO VKDSH ' VKDSH
D /( LV E /( LV F /( LV G /( LV H /( LV I /(
LV G /( LV H /( LV I /( LV J /( LV K /( LV
L /( LV :H KDYH SUHVHQWHG &216(/ D GLVWULEXWHG DQG VFDODEOH DO
JRULWKP IRU VHJPHQWLQJ '' VHQVRU QHWZRUNV 8VLQJ FRQ
QHFWLYLW\ LQIRUPDWLRQ RQO\ WKLV DOJRULWKP LV WKH ¿UVW VROXWLRQ
ZLWK ERWK ' DQG ' VHJPHQWDWLRQ FDSDELOLW\ ,Q DGGLWLRQ
WKH FRQYH[LW\ GHYLDWLRQ RI QHWZRUN UHJLRQV DIWHU VHJPHQWDWLRQ
FDQ EH ERXQGHG :H KDYH GHPRQVWUDWHG WKH HIIHFWLYHQHVV RI
&216(/ WKURXJK H[WHQVLYH VLPXODWLRQV 0RUHRYHU ZH VKRZ
KRZ VHJPHQWDWLRQ EHQH¿WV H[LVWLQJ DSSOLFDWLRQV VXFK DV JHR
JUDSKLF URXWLQJ DQG FRQQHFWLYLW\EDVHG ORFDOL]DWLRQ
,Q WKH IXWXUH LQ DGGLWLRQ WR URXWLQJ DQG ORFDOL]DWLRQ ZH
ZLOO VWXG\ LWV XVHV LQ RWKHU DSSOLFDWLRQV VXFK DV GDWD SUR
FHVVLQJ >@ >@ >@ VNHOHWRQ H[WUDFWLRQ >@ >@ DQG
HVSHFLDOO\ IRU ' VHQVRU QHWZRUNV ZKLFK KDYH DWWUDFWHG UHFHQW
DWWHQWLRQ RI PDQ\ UHVHDUFKHUV :H ZLOO DOVR VHHN PRUH HI¿FLHQW
WRROV VXFK DV DPRUSKRXV FRPSXWLQJ >@ DQG VSDWLDO FRP
SXWLQJ >@ WR FRQGXFW VLPXODWLRQV RI RXU DOJRULWKP )LQDOO\
ZH SODQ WR LPSOHPHQW RXU DOJRULWKP RQ VHQVRU QHWZRUN WHVWEHGV
WR VWXG\ LWV HI¿FLHQF\ LQ PRUH UHDOLVWLF HQYLURQPHQWV
SHUIRUP D OLQHDU WUDQVIRUPDWLRQ RQ WKHVH YLUWXDO FRRUGLQDWHV )L
QDOO\ WKH XVH RI VSULQJPDVV DOJRULWKP >@ LV DSSOLHG WR UH¿QH
QRGHV
FRRUGLQDWHV ZLWK UHVSHFW WR WKHLU QHLJKERU FRQQHFWLRQV
:H UXQ VLPXODWLRQV XVLQJ VHJPHQWDWLRQ UHVXOWV IURP
&216(/ DQG &219(; >@ )RU FRPSDULVRQ ZH
LPSOHPHQW WZR DGGLWLRQDO DOJRULWKPV )LUVW D SXUH PXOWLODW
HUDLRQ ZLWKRXW VHJPHQWDWLRQ LV HYDOXDWHG 6HFRQG &$7/ >@
D VWDWHRIWKHDUW ORFDOL]DWLRQ DOJRULWKP ZLWK ' FDSDELOLW\ LV
DOVR HYDOXDWHG 7KH NH\ LGHD RI &$7/ LV WR LGHQWLI\ QRWFK QRGHV
ZKHUH WKH KRS FRXQW RI WKH VKRUWHVW SDWK EHWZHHQ WZR QRGHV
GHYLDWHV IURP WKH WUXH (XFOLGHDQ GLVWDQFH &$7/ WKHQ XVHV
DQ LWHUDWLYH QRWFKDYRLGLQJ PXOWLODWHUDWLRQ VFKHPH WR ORFDOL]H
WKH QHWZRUN ,Q DGGLWLRQ WR VKDSH UHFRYHU\ ZH PHDVXUH WKH
ORFDOL]DWLRQ HUURU /( GH¿QHG DV WKH UDWLR RI WKH (XFOLGHDQ
GLVWDQFH EHWZHHQ WKH HVWLPDWHG ORFDWLRQ DQG LWV WUXH ORFDWLRQ
WR WKH FRPPXQLFDWLRQ UDQJH
)LJ VKRZV WKH ORFDOL]DWLRQ UHVXOWV )LUVW IRU WKH '
QHWZRUN ZH VHH D LPSURYHPHQW LQ ORFDOL]DWLRQ DFFXUDF\
>@ , ) $N\LOGL] DQG ( 3 6WXQWHEHFN ³:LUHOHVV XQGHUJURXQG VHQVRU
QHWZRUNV 5HVHDUFK FKDOOHQJHV´ Ad Hoc Netw. J. YRO QR SS
± >@ - %UXFN - *DR DQG $ $ -LDQJ ³0DS 0HGLDO D[LV EDVHG JHRPHWULF
URXWLQJ LQ VHQVRU QHWZRUNV´ Wireless Netw. YRO QR SS
± >@ 7 . 'H\ - *LHVHQ DQG 6 *RVZDPL ³6KDSH VHJPHQWDWLRQ DQG
PDWFKLQJ ZLWK ÀRZ GLVFUHWL]DWLRQ´ LQ Proc. Workshop Algor. Data
Struct. SS ±
>@ 7 (UHQ ' . *ROGHQEHUJ : :KLWHOH\ < 5 <DQJ $ 6 0RUVH %
' 2 $QGHUVRQ DQG 3 1 %HOKXPHXU ³5LJLGLW\ FRPSXWDWLRQ DQG UDQ
GRPL]DWLRQ LQ QHWZRUN ORFDOL]DWLRQ´ LQ Proc. IEEE INFOCOM SS ±
>@ $ )RPHQNR DQG 7 .XQLL, Topological Modeling for Visualization
1HZ <RUN 1< 86$ 6SULQJHU9HUODJ 7HORV >@ 5 *KULVW DQG $ 0XKDPPDG ³&RYHUDJH DQG KROHGHWHFWLRQ LQ VHQVRU
QHWZRUNV YLD KRPRORJ\´ LQ Proc. IEEE IPSN SS ±
>@ 5 +HNPDW DQG 3 9 0LHJKHP ³&RQQHFWLYLW\ LQ ZLUHOHVV DGKRF QHW
ZRUNV ZLWK D ORJQRUPDO UDGLR PRGHO´ Mobile Netw. Appl. YRO QR
SS ± >@ + -LDQJ 6 -LQ DQG & :DQJ ³3DUDPHWHUEDVHG GDWD DJJUHJDWLRQ IRU
VWDWLVWLFDO LQIRUPDWLRQ H[WUDFWLRQ LQ ZLUHOHVV VHQVRU QHWZRUNV´ IEEE
Trans. Veh. Technol. YRO QR SS ± 2FW 5()(5(1&(6
-,$1* et al. &211(&7,9,7<%$6(' 6(*0(17$7,21 ,1 /$5*(6&$/( '' 6(1625 1(7:25.6
>@ + -LDQJ 6 -LQ DQG & :DQJ ³3UHGLFWLRQ RU QRW" DQ HQHUJ\HI¿FLHQW
IUDPHZRUN IRU FOXVWHULQJEDVHG GDWD FROOHFWLRQ LQ ZLUHOHVV VHQVRU
QHWZRUNV´ IEEE Trans. Parallel Distrib. Syst. YRO QR SS
± -XQ >@ + -LDQJ : /LX ' :DQJ & 7LDQ ; %DL ; /LX < :X DQG : /LX
³&RQQHFWLYLW\EDVHG VNHOHWRQ H[WUDFWLRQ LQ ZLUHOHVV VHQVRU QHWZRUNV´
IEEE Trans. Parallel Distrib. Syst. YRO QR SS ± 0D\
>@ + -LDQJ : /LX ' :DQJ & 7LDQ ; %DL ; /LX < :X DQG : /LX
³$ JHQHUDO IUDPHZRUN IRU HI¿FLHQW FRQWLQXRXV PXOWLGLPHQVLRQDO WRSN
TXHU\ SURFHVVLQJ LQ VHQVRU QHWZRUNV´ IEEE Trans. Parallel Distrib.
Syst. YRO QR SS ± 6HS >@ + -LDQJ 7 <X & 7LDQ * 7DQ DQG & :DQJ ³&216(/ &RQQHF
WLYLW\EDVHG VHJPHQWDWLRQ LQ ODUJHVFDOH '' VHQVRU QHWZRUNV´ LQ
Proc. IEEE INFOCOM SS ±
>@ + -LDQJ 6 =KDQJ * 7DQ DQG & :DQJ ³&$%(7 &RQQHFWLYLW\EDVHG
ERXQGDU\ H[WUDFWLRQ RI ODUJHVFDOH ' VHQVRU QHWZRUNV´ LQ Proc. IEEE
INFOCOM SS ±
>@ % .DUS DQG + 7 .XQJ ³*365 *UHHG\ SHULPHWHU VWDWHOHVV URXWLQJ
IRU ZLUHOHVV QHWZRUNV´ LQ Proc. ACM MOBICOM SS ±
>@ 0 .ODQQ, Mobile Response. Chapter Tactical Navigation Support
for Fireghters: The LifeNet Ad-Hoc Sensor-Network and Wearable
System 1HZ <RUN 1< 86$ 6SULQJHU9HUODJ SS ±
>@ ) .XKQ 5 :DWWHQKRIHU < =KDQJ DQG $ =ROOLQJHU ³*HRPHWULF
DGKRF URXWLQJ 2I WKHRU\ DQG SUDFWLFH´ LQ Proc. ACM PODC SS ±
>@ % /HRQJ % /LVNRY DQG 5 0RUULV ³*UHHG\ YLUWXDO FRRUGLQDWHV IRU
JHRJUDSKLF URXWLQJ´ LQ Proc. IEEE ICNP SS ±
>@ 0 /L DQG < /LX ³5HQGHUHG SDWK 5DQJHIUHH ORFDOL]DWLRQ LQ
DQLVRWURSLF VHQVRU QHWZRUNV ZLWK KROHV´ LQ Proc. ACM MobiCom
SS ±
>@ -0 /LHQ DQG 1 0 $PDWR ³$SSUR[LPDWH FRQYH[ GHFRPSRVLWLRQ
RI SRO\KHGUD´ LQ Proc. ACM Symp. Solid Phys. Model. SS
±
>@ $ /LQJ ³7KH SRZHU RI QRQUHFWLOLQHDU KROHV´ LQ Proc. 9th Int. Colloq.
Automata Lang. Program SS ±
>@ 0,7 &DPEULGJH 0$ 86$ ³$PRUSKRXV FRPSXWLQJ´ >2QOLQH@
$YDLODEOH KWWSJURXSVFVDLOPLWHGXPDFSURMHFWVDPRUSKRXV
>@ $ 1JX\HQ 1 0LORVDYOMHYLF 4 )DQJ - *DR DQG / - *XLEDV ³/DQG
PDUN VHOHFWLRQ DQG JUHHG\ ODQGPDUNGHVFHQW URXWLQJ IRU VHQVRU QHW
ZRUNV´ LQ Proc. IEEE INFOCOM SS ±
>@ $ 3DQDQJDGDQ DQG * 6 6XNKDWPH ³'DWD VHJPHQWDWLRQ IRU UHJLRQ
GHWHFWLRQ LQ D VHQVRU QHWZRUN´ LQ Proc. DCOSS SS ±
>@ $ 5DR 6 5DWQDVDP\ & 3DSDGLPLWULRX 6 6KHQNHU DQG , 6WRLFD
³*HRJUDSKLF URXWLQJ ZLWKRXW ORFDWLRQ LQIRUPDWLRQ´ LQ Proc. ACM MobiCom SS ±
>@ 2 6DXNK 5 6DXWHU 0 *DXJHU 3 - 0DUURQ DQG . 5RWKHUQHO ³2Q
ERXQGDU\ UHFRJQLWLRQ ZLWKRXW ORFDWLRQ LQIRUPDWLRQ LQ ZLUHOHVV VHQVRU
QHWZRUNV´ LQ Proc. IPSN SS ±
>@ $ 6DYYLGHV && +DQ DQG 0 % 6WULYDVWDYD ³'\QDPLF ¿QHJUDLQHG
ORFDOL]DWLRQ LQ DG KRF QHWZRUNV RI VHQVRUV´ LQ Proc. ACM MobiCom
SS ±
>@ * 7DQ 0 %HUWLHU DQG $0 .HUPDUUHF ³&RQYH[ SDUWLWLRQ RI VHQVRU
QHWZRUNV DQG LWV XVH LQ YLUWXDO FRRUGLQDWH JHRJUDSKLF URXWLQJ´ LQ Proc.
IEEE INFOCOM SS ±
>@ * 7DQ + -LDQJ 6 =KDQJ DQG $0 .HUPDUUHF ³&RQQHFWLYLW\EDVHG
DQG DQFKRUIUHH ORFDOL]DWLRQ LQ ODUJHVFDOH '' VHQVRU QHWZRUNV´ LQ
Proc. ACM MobiHoc SS ±
>@ % 7HFKQRORJLHV ³6SDWLDO FRPSXWLQJ´ >2QOLQH@ $YDLODEOH KWWS
SURWREEQFRPFRPPRQV
>@ 6 ;LD ; <LQ + :X 0 -LQ DQG ; ' *X ³'HWHUPLQLVWLF JUHHG\
URXWLQJ ZLWK JXDUDQWHHG GHOLYHU\ LQ ' ZLUHOHVV VHQVRU QHWZRUNV´ LQ
Proc. ACM MobiHoc $UW QR >@ + =KRX 1 'LQJ 0 -LQ 6 ;LD DQG + :X ³'LVWULEXWHG DOJRULWKPV
IRU ERWWOHQHFN LGHQWL¿FDWLRQ DQG VHJPHQWDWLRQ LQ ' ZLUHOHVV VHQVRU
QHWZRUNV´ LQ Proc. IEEE SECON SS ±
>@ ; =KX 5 6DUNDU DQG - *DR ³6KDSH VHJPHQWDWLRQ DQG DSSOLFDWLRQV
LQ VHQVRU QHWZRUNV´ LQ Proc. IEEE INFOCOM SS ±
>@ ; =KX 5 6DUNDU DQG - *DR ³7RSRORJLFDO GDWD SURFHVVLQJ IRU GLV
WULEXWHG VHQVRU QHWZRUNV ZLWK 0RUVH6PDOH GHFRPSRVLWLRQ´ LQ Proc.
IEEE INFOCOM SS ±
+RQJER -LDQJ 0
UHFHLYHG WKH %6 DQG 06 GH
JUHHV LQ DSSOLHG PDWK IURP +XD]KRQJ 8QLYHUVLW\ RI
6FLHQFH DQG 7HFKQRORJ\ :XKDQ &KLQD LQ DQG
UHVSHFWLYHO\ DQG WKH 3K' GHJUHH IURP &DVH
:HVWHUQ 5HVHUYH 8QLYHUVLW\ &OHYHODQG 2+ 86$
LQ $IWHU WKDW KH MRLQHG WKH IDFXOW\ RI +XD]KRQJ 8QL
YHUVLW\ RI 6FLHQFH DQG 7HFKQRORJ\ DV DQ $VVRFLDWH
3URIHVVRU +LV UHVHDUFK FRQFHUQV FRPSXWHU QHW
ZRUNLQJ HVSHFLDOO\ DOJRULWKPV DQG DUFKLWHFWXUHV IRU
KLJKSHUIRUPDQFH QHWZRUNV DQG ZLUHOHVV QHWZRUNV
7LDQORQJ <X 6
UHFHLYHG WKH %6 GHJUHH LQ FRP
SXWHU VFLHQFH IURP +XD]KRQJ 8QLYHUVLW\ RI 6FLHQFH
DQG 7HFKQRORJ\ +867 :XKDQ &KLQD LQ DQG
LV FXUUHQWO\ SXUVXLQJ WKH 06 GHJUHH LQ HOHFWURQLFV
DQG LQIRUPDWLRQ HQJLQHHULQJ DW +867
+LV FXUUHQW UHVHDUFK DUHDV LQFOXGH ZLUHOHVV DQG
VHQVRU QHWZRUNV
&KHQ 7LDQ 0
UHFHLYHG WKH %6 06 DQG
3K' GHJUHHV LQ OHFWURQLFV DQG LQIRUPDWLRQ HQJL
QHHULQJ IURP WKH +XD]KRQJ 8QLYHUVLW\ RI 6FLHQFH
DQG 7HFKQRORJ\ :XKDQ &KLQD LQ DQG
UHVSHFWLYHO\
+H MRLQHG WKH IDFXOW\ DV D /HFWXUHU ZLWK WKH 'HSDUW
PHQW RI (OHFWURQLFV DQG ,QIRUPDWLRQ (QJLQHHULQJ
+XD]KRQJ 8QLYHUVLW\ RI 6FLHQFH DQG 7HFKQRORJ\
+LV UHVHDUFK LQWHUHVWV LQFOXGH GLVWULEXWHG QHWZRUNV
DQG ZLUHOHVV QHWZRUNV
*XDQJ 7DQ 0
UHFHLYHG WKH 3K' GHJUHH LQ
FRPSXWHU VFLHQFH IURP WKH 8QLYHUVLW\ RI :DUZLFN
&RYHQWU\ 8. LQ +H LV FXUUHQWO\ DQ $VVRFLDWH 3URIHVVRU ZLWK WKH
6KHQ]KHQ ,QVWLWXWH RI $GYDQFHG 7HFKQRORJ\ 6,$7
&KLQHVH $FDGHP\ RI 6FLHQFHV 6KHQ]KHQ &KLQD
ZKHUH KH ZRUNV LQ WKH DUHD RI GLVWULEXWHG V\VWHPV DQG
QHWZRUNV )URP WR KH ZDV D 3RVWGRFWRUDO
5HVHDUFKHU ZLWK ,15,$5HQQHV 5HQQHV )UDQFH
'U 7DQ LV D PHPEHU RI WKH $VVRFLDWLRQ IRU &RP
SXWLQJ 0DFKLQHU\ $&0
&KRQJJDQJ :DQJ 0
±60
UHFHLYHG WKH 3K'
GHJUHH LQ FRPSXWHU VFLHQFH IURP %HLMLQJ 8QLYHUVLW\
RI 3RVWV DQG 7HOHFRPPXQLFDWLRQV %HLMLQJ &KLQD LQ
+H KDV FRQGXFWHG UHVHDUFK ZLWK 1(& /DERUDWRULHV
$PHULFD 3ULQFHWRQ 1- 86$ $77 /DEV 5HVHDUFK
0LGGOHWRZQ 1- 86$ WKH 8QLYHUVLW\ RI $UNDQVDV
)D\HWWHYLOOH $5 86$ DQG +RQJ .RQJ 8QLYHUVLW\
RI 6FLHQFH DQG 7HFKQRORJ\ +RQJ .RQJ +H KDV SXE
OLVKHG PRUH WKDQ MRXUQDOFRQIHUHQFH DUWLFOHV DQG
ERRN FKDSWHUV +LV UHVHDUFK LQWHUHVWV LQFOXGH IXWXUH
,QWHUQHW PDFKLQHWRPDFKLQH 00 FRPPXQLFDWLRQV DQG FRJQLWLYH DQG ZLUH
OHVV QHWZRUNV
© Copyright 2026 Paperzz