An O(n1.5) Deterministic Gossiping
Algorithm for Radio Networks
Ying Xu
田文錦
Radio Network
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1.All processor work synchronously
and have unique identifiers
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2.Message collision
3.Assume strongly connected
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Two Problems
Broadcasting problem
One distinguished source node has a message that
needs to be sent to all other nodes.
Gossiping problem
Each node is initially given a different message that
needs to be distributed to all other nodes.
每個processor在發送message 的
時候是把自己和之前收到的一起
發送給所有相鄰的processor
Round Robin Algorithm
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Time Complexity
O(Dn) = O(n2)
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An O(n1.5logn) Time Gossiping Algorithm
1. For every node v collate informatio n about its in - neighnorho od
N r (v) of radius r by running Round - Robin procedure r times.
2. Choose a central node  among all nodes.
D
3. For i  1,...,   do
r
(a) Process informatio n received by  so far and store it in a graph
representa tion Gir ( ) which is a union of some paths of G directed
to  covering all nodes within inradius ir form .
(b) Distribute Gir ( ) to all nodes in the network using determinis tic
broadcasti ng.
(c) With a help of Gir ( ), collate informatio n from in - neighborho od
of  of radius (i  1)r by sending N r (v) of every node v at distance ir
from  to .
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2 times round robin
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Analysis
rn
1. For every node v collate informatio n about its in - neighnorho od
N r (v) of radius r by running Round - Robin procedure r times.
2. Choose a central node  among all nodes.
D
3. For i  1,...,   do
忽略
r
(a) Process informatio n received by  so far and store it in a graph
representa tion Gir ( ) which is a union of some paths of G directed
to  covering all nodes within inradius ir form .
B(n) = O(nlogn)
(b) Distribute Gir ( ) to all nodes in the network using determinis tic
broadcasti ng.
O(n)
(c) With a help of Gir ( ), collate informatio n from in - neighborho od
of  of radius (i  1)r by sending N r (v) of every node v at distance ir
from  to .
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O(n1.5) Time Algorithm
B(n) = O(nlogn)
1. Node 1 initiates a determinis tic broadcast. Each node v collects
informatio n p (1, v);
rn
2. Run Round Robin for r rounds. Each node v collects informatio n
about N r- (v), as well as p (1,u ) for any u  N r- (v);
3. For i  1,...,D/r  do
忽略
(a) Node 1 constructs Tir- (1) and Tir (1);
O(n)
(b) Node 1 distribute s Tir- (1) and Tir (1) to all nodes in N ir- (1);
O(n)
(c) Each node in N ir- (1) sends N r- (v) and p (1,u ) for any u  N r- (v),
as well as its initial message, back to 1;
4. Node 1 distribute s all message it collected to all nodes.
O(n)
Reference
L. Gasieniec and A. Linags, On adaptive deterministic gossiping in
ad hoc radio networks, Inform. Process. Lett., 2(2002),89-93
M. Chrobak, L. Gassieniec, and W. Rytter, Fast broadcasting and
gossiping in radio networks, in Proc. 41st IEEE Symposium on
Foundations of Computer Science, 200, pp575-581