- An English-Persian Dictionary of Algorithms and Data Structures a a ! "#$ [email protected] [email protected] 1381 ( ! 23 algorithm B all pairs shortest path :::::::::::::::::::::::: A absolute performance guarantee b alphabet alternating path alternating Turing machine alternation amortized cost amortized worst case ancestor and ANSI antichain antisymmetric approximation algorithm arc array array index array merging articulation point articulation vertex assignment problem association list associative ;'< $(.= :::::::::::::::::::::::::::::::::: :::::::::::: :::::::::::::::::::: > #( !"(6 ::::::::::::::::::: : ::::::::::::::::::::::::::::::: ::::::::::::::: :::: !" # $% ::::::::::::::::::::::::::::::::::: & d :::::::::::::::::::::::::::::::::::::::::: ::::::::::::::: abstract data type accepting state Ackerman's function Ackermann's function acyclic digraph acyclic directed graph acyclic graph adaptive heap sort adaptive k-d tree adaptive sort address-calculation sort adjacency-list representation adjacency-matrix representation ::::::::::::::::: d @ :::::::::::::::: d @ ::::::::::::: $A& B 6 :::::: $A& B 6 ::::::::::::::::::::::: :::::::: ' ( !" ::::::::::::::::::::::::::::: b ::::::::::: )(*+ , -+ : :::::::: - ::::::::::::::::::::::::::::::::::::::: ,. ::::::::::::::::::::::::::::::::::::: " / C -< ! $D -< * / 6" E * C C F ) $ G.( F ) 0 G.( ::::::::::::::::::::::::: adjacency list adjacency matrix adjacent admissible vertex adversary algorithm " / 0( :::::::::::::::::::: ::::::::::::::::::::::: " / 12 ::::::::::::::::::::::: 34 d :::::::::::::::::::::: 34 d ::::::::::::: ::::::::::::::: F ) $ F ) 0 ::::::::::::::::::::::::::::::::: 5.6 !"'7 ::::::::::::::::::::: ) *) b :::::::::::::::::::::::::::::::: ::::::::::::::: :::::::::::::::: B 6 -< * ::::::::::::::::::: :::::::::::::::::::::::: ?8+ $% ! 8+$ $ :::::::::::::::::::::::::::::: (.)( ) ! 8+$ 1 CH binary function binary GCD algorithm binary insertion sort binary priority queue binary relation binary search binary trie bingo sort bipartite graph bipartite matching bisector bit vector block blocking ow blossom boolean boolean expression boolean function bottleneck traveling salesman ::::::::::::::::::::: ::::: associative array asymptotic bound asymptotic lower bound asymptotic space complexity @ ::::::::::::::::: 11 :::::: & * :::::::: :::::::::::::::::: C ::::::: $ IJ :::::::::::::::::: :::::::::::::::: !"< ! c :::::::::::::::::::::::: * ::::::::::::::::::: C KL ;< ::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::: * :::::::::::::::::::: ( :::::::::::::::::: :: () ;H , K #? (D ) , ::::::::::: "? , ! * T T $% P c!! c $D B @ B+-tree backtracking bag balance balanced binary search tree ::::::::::::::::::::::::: N " + * U+ $D :::::::::::::::::::::::::::: ::::::::::::::::::: C 60+ ("(6V !">.)) " 6 :::::::::::::::::::::::::::::::::: N " + D , boundary-based representation :::::::::::::::::::: ::::::::::::::::::: ::::::: , IJ P Q< a :::::::::: ::::::::::::::::::::::: balanced merge sort balanced multiway merge balanced node balanced quicksort balanced two-way merge sort :::::: % OK( :::::::::::::::::::::::::::::: C 3+ :::::::::::::::::::::: :::::::::::::::::::::: :::::::::::::::::::::: :::::::::::::: '< '< C !3< C , * 2 * C ::::: ?-.' 5 ::::::::: :: . !" b . B 6 "A& % * :::::::::::::::::::: ::::::::::::::::::::::::: 2 $% A P A !&$& a :::::::::::::::: C ? ,(H $% A !" # ::::::::::::: !" / , * !6 , * @ :::::::::::::: 3< * , * V 12 :::::::::::::::::::::::::: + $D ::::::::::::::::::::::::::::::::::: C :::::::::::::::::::::: "( % * , * 2 * * Bellman-Ford algorithm Benford's law best-case best-case cost best rst search biconnected component biconnected graph bidirectional bubble sort big-O notation bin sort '( !* :::::::::::::::::::::::: C ::::::::: 1A(* :::::::::::::::::::::::::::: 2 * ::::::::::::::::::::: !&$& :::::::::::::::::::::::::::::::::::::: k :: OK( KD * , * $D , * - , !"K+ ::::::::::::::::: ::::::::: , * , * !&$& $D balanced binary tree balanced k-way merge sort "( G.( bounded queue bounded stack branch and bound branching breadth rst search Bresenham's algorithm brick sort bridge British Museum algorithm brute force BSP-tree bubble sort bucket bucket array bucket sort bucketing method Byzantine Agreement Problem " $% !" # :::::::::::::::::::::::: 6'6 6 ! ? bottom-up radix sort bottom-up tree automaton :::: () ! ::::::::::::::::::::::: F> :::::::::::::::::::::: () !N , ::::::::: ! ( ! ::::::::::::::::::::::::::::::::::: :::::: ::::::::::::::: M' ::::::::::::::::::::::::::::::::: () (* 6S+ :::::::::::::::::: !" / :::::::::::::::::::::::::::::::::::: () + , :::::::::: KL B 6 ::::::::::::::: () , () !"R?% 6S+ asymptotic time complexity asymptotic upper bound asymptotically equal to asymptotically tight bound augmenting path automaton automaton simulation average-case average-case cost AVL tree !&$& ::::::::::::::::::::::::: .)( !" / C X # !e .( c '< * C competitive ratio complement complete binary tree complete graph complete tree complexity complexity class computable computable function concave function concurrent ow conguration conjunction connected component connected graph coNP constant function continuous knapsack problem ::::::::::::::::::: H $( ::::::::::::::::::::::::::::: :::::::: ::::::::::::::::: Calculus of Communicating Systems 6S+ \ ! 6S+ ! ::::::::::::::::::::::::: ::::::::::::: 8+" 8+" :::::::::::::::::::::: ::::::::::::::::::: ::::::::::::::::::::::: ::::::::::: ((() BO 6S+ ! E @ capacitated facility location O- @ E $?] FUA , capacity capacity constraint cell probe model cellular automaton centroid certicate chain child Chinese postman problem Chinese remainder theorem :::::::::::::::::::::::::::::::: ! + :::::::::::::::::: <> C ::::::::::::::: . !" b :::::::::::::::::::: ::::::::::::::::::::: $Y @ :::::::::::::::::: M G . * ::::::::::::::::::::::::::: :::::::::::::::::::: ::::::::::::::::::: :::::::::::::::::::::::::::::::::::: )(* :: :::::::: 5 !" ::::::::::::::::::: ( ^D :::::::::::::::::::: :::::::::: !"ZH -_ V # ::::::::: DAG shortest paths :::::::::::::::::::::::::::: !-'% $ ::::::::::::::::::::: :::::::::::::::::::: 8+.4 8+.4 , * :::::::::::::::: .4 !"'7 !-'% IJ :::::::::::::: :::::::::::::::::::::: "D "D !"'7 O.) $K6* ::::::::::::::::::::::::::::::::: .4 $D ! "( * 14 C T !* + commutative comparison sort competitive analysis 8+" #) !&$& !"'7 :::::::::::::::::::::::::::::::::::: ! :::::::::::::::::::::::::::::::::::: + :::::::::::::: :::::::::::::::::::::: degree 5* !"'7 :::::::::::::::::::::::: $A& B 6 6S+ ::::::::::::::::::::::: :::::::::::::::::::::::::::::: ( > :::::::::::::::::::::::::::::::::::: D D (* ? V S+ !"'7 :::::::: !"EJ ::::::::::::::::::::::: 3-Y # 6 ::::::::::::::::: data structure database decidable decidable language decision problem decision tree decomposable searching problem , ::::::::::::::::::::::::::::::: Christodes algorithm Christodes heuristic chromatic index chromatic number Church-Turing thesis circuit circuit complexity circuit value problem circular list circular path circular queue clique clique problem collective recursion collision comb sort Communicating Sequential Processes b :::::::::::::::::::::::::::::::::::::: ' V !(H !"ZH C ( E !"'7 ::::::::::::::::::::::::::::::::::::::: P ::::::::::::::::::::::::::::::::::::: M !"ZH ::::::::::::::::::::: ::::::::::::::::::::::::::::::: +, c + K+" !"'7 ::::::::::::::::::: $?] $?] H P' ::::::::::::::: . B 6 :::::::::::::::::::::::::::::::::: ,% canonical complexity class E ,* ! ::::::::::::::::::::::::: !P ([ C 3 $D :::::::::::::::::::::::::::: ::::::: :::::::::::::: 3 B 6 ::::::::::::::::::::::: Cook's theorem Cook reduction counting sort critical path problem cut cut vertex cutting plane cutting theorem cycle Byzantine generals 3. 3 $D :::::::::::::::::::::: " !O !"'7 ::::::::::::::::::::::::: "& :::::::::::::: 3 &"& ! "- * ::::::::::::::: C H 3'E distributional complexity divide and conquer divide and marriage before conquest ::::::: degree-k graph delete dense graph depth depth rst search deque derangement descendant deterministic deterministic algorithm deterministic nite automaton O * 6S+ :::::::::::::::::: 3%- :::::::::::::::::::::::: domain Doomsday rule double-direction bubble sort ::::::::::::::::::::::::::::::::::: (.* ) #D " ::::::::::: ::::::::::: I c J :::::::::::::::::::::: ::::::::::::::::: ::::::::::: + :::: O<H deterministic nite state machine O<H $% deterministic nite tree automaton + $D ! * O<H O<H $% , + ! # "( :::::::::::::::::::::::: ( deterministic nite state automaton + !" / + ! * G + O<H , ,6 ::::::::::::::::::::::::::::::::::: O<H D , deterministic pushdown automaton + 3 O<H ! "K+ , E deterministic tree automaton Deutsch-Jozsa algorithm DFS forest diagonalization diameter dictionary dierence digraph Dijkstra's algorithm diminishing increment sort dining philosophers directed acyclic graph directed acyclic subsequence graph O<H D , edge edge coloring edge connectivity edge crossing eciency element uniqueness EM data structure Euclid's algorithm Euclidean algorithm Euclidean distance Euclidean Steiner tree Euclidean traveling salesman problem :::: ::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::: P ::::::::::::::::: :::::::::::::: :::::::::::: 'H 'H ::::::::::::: 'H !"'J? :::::: 'H $D :::::::::::::::::::::::::: ! ' ::::::::::::::::::::::::::: ! ' ::::::::::::::::::::: ! ' B 6 :::::::::::::::::::::: ! ' ZO * :::::::::::::::: ! "( * " C 6 !B'? $A& B 6 directed graph discrete p-center disjoint-set data structure :::::::::::::::::::: :::::::::::::::: disjoint-set forest disjoint set disjunction distribution sort C "6 #- :::::::::: 4 #) !">.) :::::::::::::::::::::::: B 6 p #) !">.) 3& :::::::::::::::::::::: !& $% "O $A& B 6 #) !">.) D (@.) @() ! 4E( ! ::::::::::::::::::: $A& !"( * B 6 'H 6 ! ? !"'7 :::::::::::::::::: 3= $A& B 6 :::::: ::::::::::: <H ! ? :::::::::::::::::::::::::: , ! <H ::::::::::::::::::::::::::::::: Z> :::::::::::: :::::::::::::::::::::::: &D !"R?% D P ;.> !&$& 3& a :::::::::::::::::::::::::::::::::: @\- :::::::::::::::::::::::::::::::: * &-` ::::::::::::::::::::: !. :::::::::::::::::::::::: ::::: :::::::::::: ! #/( :::::::::::::::::: ::::::::::: IJ ::::::::::::::::::::::::::::: "?\ !(+ $ ::::::::::::::::::::::::::::::::::::: Euler cycle Euler tour Eulerian graph Eulerian path exchange sort exclusive or existential state expander graph :::::::::::::::::::::::::::::::: I>Z , :::::::::::::::::: ;.> P ;.> !&$& a ::::::::::::::::::::::::::::::: C I>Z ! * :::::::::::::::::: :::: B 6 ::::::::::::::::::::::::::::: :::::::::::::: ::::::::::: B8% ::::::::::::::::::::::::::::::::::::: * ,(H "A& % * double hashing double rotation doubly-ended queue doubly linked list dual dynamic dynamic array dynamic hashing dynamic programming dynamic tree dynamization transformation "& B 6 :::::::::::::::::::::::::::::::::::: 3% * G+ C - :::::: k :::::::::::::::::::: :::::::::::::::: '4? C O * * C formal language formal methods formal verication fractal fractional knapsack problem :::::::::::: (. ::::::::::::::::: ::::::::::::: exponential extended Euclid's algorithm ) ! J , * . :::::::::::::::::::::::::::::: !5 . ::::::::::::::::::::::::::::::::::: "?56 'H external memory algorithm P? &D !"R?% external memory data structure 8+- K+" !"'7 fractional solution free edge free vertex full array full binary tree fully dynamic graph problem ::::::::::::::::: ! & ::::::::::::::::::::::::::::::: &D !"R?% D external merge external merge sort external quicksort external radix sort external sort extreme point */ P :::::::::::::::::::::::::::: */ b ::::::::::::::::::::::::::::: + !" / ::::::::::::::::: :::::::::::::::::::: + $D :::::: ::::::::: &D @ :::::::: f B 6 !"'7 + U c 6(1. D C &D * C facility location factorial feasible region feasible solution feedback edge Ferguson-Forcade algorithm ::::::::::::::: :::::::::::::::::::::::::: ! *? !6 ::::::::::::::::::::::::::::: FUA , ::::::::::::::::: ! *? P ! *? B 6 :::::::::::::: 8+, & ( D0+) D* P e - ? Fibonacci number Fibonacci numbers nite automaton nite Fourier transform nite state automaton nite state machine nite state machine minimization G ::::::::::::::::: ::::::::::::::::::::::: ! * global optimum graph graph coloring graph drawing graph isomorphism graph partition greatest common denominator ::::::::::::::::: 6 @ "A !"'7 ! :::::::::::::::::::::::::::::::::::: ::::::::::::::::: B 6 ::::: !" ? 3 :::::: $% , $% ::::::::: ::::: B 6 * ? & D -! :::::::::::::::::::::::: $Y ! 5 c !+ * C ::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::: MK "'>1- X # :::::::::::::: :::::::::::::: ::::::::::::::::::::::: "(4 % !" (! ! ) ! " :::::::::::::::: !- :::::::::::::::::::::::::: "(4 % : @ !" P -'? ::::::::::::::::::::::: 6 c :::::: .'- ? c ?- ? 5 :::::::::::::::::::::::::::::::::::: 5 ". $% P :::::::::::::: MK hL X # ::::::::: , nite state transducer rst-in, rst-out xed-grid method ash sort ow ow conservation ow function ow network Floyd-Warshall algorithm Ford-Bellman Ford-Fulkerson method forest greatest common divisor greedy algorithm greedy heuristic grid drawing Grover's algorithm ::::::::::::::::: $% ! * B 6 L g ::::::::::::::::::::::: V(? > V(? > :::::::::: B 6 6? ::::::::::::::: B 6 ! #/( :::::::::::::::::::::: ::::::::::: !"A 3 ? 8+, !"%( ::::::::::::::::: ! *? @ gamma function geometric optimization problem C e !"<-( i ::::::::::::::::::::::::::::::: @ ::::::::::::::::::::::::: &D * F f C - !. ! "'.&V U :::::::::::::::::::::::::::: C * :::::::::::::::::::::: fully polynomial approximation scheme ::::::::::::::::::::::::::::::::::: &D 12 &D 2 * :::::::::::::::::::: fully persistent data structure function fuzzy edge fuzzy graph fuzzy node fuzzy set .( 3& interactive proof system interior-based representation internal node internal path internal sort interpolation sort intersection interval tree intractable intro sort introspection sort introspective sort irreexive isomorphic iteration ::: H ! E FY halting problem Hamiltonian cycle hash hash function hash table Hausdor distance head heap sort Herter-Heighway Dragon heuristic hidden Markov model histogram sort homeomorphic homomorphic horizontal visibility map Horner's rule hybrid algorithm hyperedge hypergraph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j :::::::::::: * :::::::::::::::: C $L -? !"K-( :::::::::::::::::::::::: :::::::::::::::::::::::::::::::: ( ,(H "L/ ::::::::::::::::::::::::::::::: ,(& ::::::::::::::::::::::::::::: K k-coloring k-dimensional k-way merge k-way merge sort Karnaugh map Karp reduction key Koenigsberg bridges Koenigsberg bridges problem :::::::::::::::::::::::: ! #/(- ::::::::::::::::::::::::: ::::::::::::::::::::: ::::::: - k k 2 * :::::::::::::::::::::::: ::::::::::::::::::::: j G ::::::::::::::::::::::::::::::::::::::: P/ 12 :::::::::::::::::::::::::::: ' ! OK( :::::::::::::::::::::::: ! !"& C, G.+ :::::::::::::::::::::: ::::: :::::::::::::::: ::::::::::: :::::::: $? !( :::::::::::::::::: k ::::::::::: :::::::::::::::::::: !" V(? > k ! c .( -< ! 3- !">.) C, G.+ & * ::::::::::: e ::::::::::::::::::::::: P. a 3J >U\ !" R( , :::::::::::::: 1 e C (K(K? !" ::::::::::::::: gk D c P ::::: & 12 & * ::::::::::::::::::::::::: B 6. 6S+ ")( ::::::::::::::::::::: X( !3+ 1 #' ::::::::::::::::::::: :::::::::::::: X( !3+ !"'7 Kolmogorov complexity Kraft's inequality Kripke structure Kruskal's algorithm kth order Fibonacci numbers B 6 :::::::::::::::::::::::::::::: C ( !"K-( :::::::::: ideal merge implication implies in-branching in-degree in-order traversal in-place merging in-place sort inclusion-exclusion principle inclusive or incompressible string independent set information theoretic bound inorder traversal insertion sort instantaneous description integer multi-commodity ow 12 ::::::::::::::::::::: P I k k !O- - C $L ,. ::::::::::::::::::::::::: J C L B P ::::::::::::::::::::: :::::::::::::::::::::::::::::::::: !- ![ c ::::::::::::::::::::::::::::: :::::::::::::: kth shortest path KV diagram @ ::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::: j sort Johnson's algorithm IH !"'7 C (/ IJ QEJ NV ! integer polyhedron 6 :::::::::::: QEJ A&V median memoization merge merge sort meromorphic function min minimal antichain decomposition ::::::::::::::::::::::::::::::::::: :::::::::::::::::::::: ! k L "( l-reduction labeled graph language last-in, rst-out lattice layered digraph layered graph least common multiple linear linear insertion sort linear order linear probing sort linear product link linked list list little-o notation Lm distance logarithmic Lotka's law lower bound lower triangular matrix \D" 12 ::::::::::::::::::: :::::::::::::::::::::: 2 * C g? @ :::: :::::::::::::::::::::::::::::::::::::: ". :::::::::::: (6 3< gV minimum code spanning tree e 6 ? $D :::::::::::::::::::::::::::::::::::: <D :::::::: C <D & * <D C <D * :::::::::::::::::::::: :::::::::::::::::::::::: ". 5 ". 6 ? $D ::::::::::::::::::::::::: ". b 5 ::::::::::::::::::::: P e Lm ::::::::::::::::::::::: :::::::::::::: " E P ::::::::::::::::::::::::::: ::::::::::::: U .( $D #( N ,(H :::::::::::::::::::::::::: ::::::: $D !OJ :::::::::::::::::::::: :::::::::::::::::::::::::::: :::::::::: ::::::::::::::::::::: NV ! Manhattan distance many-one reduction Markov chain matched edge matched vertex matching matrix max maximal independent set maximally connected component "(6V !">.) ::::::::::::::: ::::::::::::: "(6V B 6 " V .4 :::::::::::::::::: + , m'm+ 0 M (P-( ) $% :::::::::::::::::::::::: ::::::: V 12 A !"'J? :::::::::::: g"V G :::::::::::::::::: B !)(* ::::::::::::::::::::: :::::::::::::::::: N "?;< P "?;< b :::::::::::::::::::::::::::::::: n-ary function NC many-one reducibility :::::::::::::::::::::: - n !"'J? . :::::::::::::::::::::::::: :::::::: $ gV !e .( c :::::::::::::::::: (+ !(+ $ :::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::: C <D = :::::::::::::::::::::::::::::::::::::: ::::::: :::::::::::: ::::::::::::::::::::::::::::::::: @ ::::::::::::::::::::::::::::::::::::: ;< 0 "K "K 3- !">.) , g"V ! 8+G nearest neighbor search maximum-ow problem maximum bipartite matching ". g#( !&$& :::: ::::::::::::::::::::::::::: (() l-( ::::::::::::::::::::::: " ! .P. # !" b "K ! !"'7 "K KL ;< ::::::: Mealy machine mean " ! !"'7 :::::::::::::::::::::::::::: ::::: MK Z gV ::::::::: " # 6 ? $D negation network ow network ow problem next state NIST "N B 6 ::::::::::::::::::::::::: minimum cost spanning tree " "N $A& B 6 ::::::::::::::::::::: minimum bounding box , * & D -! D/ :::::::::::::::::::::::::::::::::::: P. ! )(*+ !" #) G CV B 6 :::::::::::::::::::::::::::::::::: ::::::::::: minimum cut minimum spanning tree minimum vertex cut mode model checking model of computation moderately exponential monotonically decreasing monotonically increasing Moore machine move multi-commodity ow multi-set multigraph multiway decision multiway merge l ::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::: / ! /? ( O $% ::::::::::::::::::::: ' :::::::::::::::::::::::::::::::::: ' !" b 7 ( optimal triangulation problem node nonbalanced merge nonbalanced merge sort nondeterministic nondeterministic algorithm nondeterministic nite automaton ::::::::::::::::::::::::::::::::::::::: "A !n'm !"'7 optimal value optimization problem or oracle set oracle tape oracle Turing machine order ordered binary decision diagram :::::::::::::::::::::::: :::::::: ! * "A - , * ( 2 * :::: 6G+ ( :::::: C O<H2 $% O<H2 D , nondeterministic polynomial time C !(+ $ $A& B 6 :::::::::::::::::::: O<H2 ! "'.&V ,* nondeterministic tree automaton $A& B 6 :::::::::::::::: O O<H2 D , nondeterministic Turing machine E f O !.>--? O'=V ( ( 2 * O<H2 noniterative merge not NP-complete language nullary function C ::::::::::::::::::: & D OK( :::::::::::::::::::::: & D !"& :::::::::::::: ::::::: p - :::::::::::::: ::::::: 2 * :::::::::::::::::::::::::::::: " $( V ::::::::::: 1. +, , * O O notation o notation objective function o-line algorithm omega omicron on-line algorithm one-dimensional optimal optimal cost optimal merge optimal polygon triangulation problem ! + !&$& ::::::::::::::::::::::: ::::: J @ O C 86"N PN :::::::::::::::::::::: #& @ :::::::::::::::::::::::::::::::: X # !e .( c ::::::::::::::::::::::: X # !e .( c gV !e .( c ::::::::::::::::::::::: #& C :::::::::::::::::::: #& K6* @ :::::::::::::: B @ TD, ::::::::::::::::::::::::::::::::::::: f o#& !"'7 8+.4 ::::::::::::::::::::::::::::::: partially dynamic graph problem ::::::::::::::::: + #& B 6 !"'7 ::::::: C #& !">.) :::::::::::::::::::::::::::::::::::::: :::::::::::::::::::: ::::::::::: :::::::::::::::::: :::::: ::::::::::::::::::::::: ::::::::::::::::::::::: 3 ;< !O-g e "A "A !" # "A 12 O'=V !"A !n'm !"'7 optimal polyphase merge optimal polyphase merge sort $(.= : $( 6( D , e ::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::: 6( #& D e TD :::::::::::::::::::: partially ordered set partially persistent data structure path perfect matching performance guarantee performance ratio persistent data structure planar graph planar straight-line graph ! 2 12 ::::::::::::::::::: P p-way merge sort padding argument parametric searching partial function partial order partial recursive function partially decidable problem O<H2 nondeterministic nite state machine C .4 .( :::::::::::: :::: O<H2 nondeterministic nite tree automaton ordered linked list oriented acyclic graph oriented graph orthogonal drawing orthogonally convex rectilinear polygon oscillating merge sort out-branching out-degree C O<H2 , 6G+ :::::::::::::::::::::::::::::::::::: , * ( 12 :::::::::::::::::::::: 6G+ !">.) :::::::::::::::::::::::::: ::::: : "A !"'7 ::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::: :::::::::::::::: 6 "A ! "'%V 12 "A ! "'%V 2 * optimal solution Q< B 6 8 ::::::::::::::::::::: C "A & pseudorandom number pth order Fibonacci numbers :::::::::: ?4" > - p<D Q< B 6 planarity planarization pointer machine poissonization polyhedron polylogarithmic polynomial polynomial-time algorithm ::::::::::::::::::::::::::: p 1 e purely functional language pushdown automaton pushdown transducer !" V(? > :::::: f , * O U ::::::::::: ! "K+ , :::::::::::::: ::::::::::::::::::::::: ::::::::::::::::::::: ,( :::::::::::::::::::: ::::::::::::::::::::::::::: q qm * C * C ! "'.&V ! "'.&V,* polynomial-time approximation scheme ! "'.&V,* C - !. polynomial-time Church-Turing thesis AV $D 6S+ !"ZH ::::::::: .( !" :::::::::::::::::::::::::::::::::::: E ! "'.&V,* -_ V # polynomial-time reduction polynomial approximation scheme IJ :::::::::::::::::::::::: @ * C ::::::::::::::::::::::::: @ * C ! "'.&V,* G ! "'.&V C - !. polynomial hierarchy polynomial time polyphase merge polyphase merge sort poset Post's correspondence problem postman's sort potential function Prim's algorithm primitive recursive priority queue prisoner's dilemma probabilistic algorithm probabilistic Turing machine :::: R ! "'.&V C "'' ::::::::::::::: :::::::::::::: :::::::::::: + A&V . V ::::::::::::::::::::::::: ::::::::::::::::::::::::::::::: Q< 6 :::::::::::::::::::::::::: ! "K+ P q sort qm sort quadtree complexity theorem r.e. language radix sort ragged matrix random access machine random number random number generator randomization randomized algorithm randomized complexity randomized rounding range range sort reachable recognizer rectangular matrix rectilinear rectilinear distance rectilinear Steiner tree recurrence equations recurrence relation recurrences recursion recursion termination ! * :::::::::::::::::: Q quantum computation queue quick sort quicksort , Q< 8+5.K6* , * ::::::::::::::::::::::: * ::::::::::::::::::: :::::::::::::::::: :::: $ ! "'%V 12 ! "'%V 2 * C :::::::::::::::::::::: .( 0 ?4 ! "'.&V ,* C #& !">.) $+ ] !"'7 ::::::::::::::::: ?4 > S+ * ::::::::::::::::::: ?4 > :::::::::::::::::: :::::::::::::::::::: ! * ?4 ::::::::::::::: :::::::::: ?4 :::::::: ?4 6S+ :::::::::: ?4 , 6 :::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::: ! * * ::::::::::::::::::::::::: $ :::::::::::::::: ::::::::: C C 3(+ @ + 'J K6* :::::::::::::::::::::: e C $ IJ , !.O .% .% :::::::::::::: ( probabilistically checkable proof 3H ) ^LK .% 8+ ::::::::: :::::::::::::::::::::::: :::::::: procedure process algebra proper proper coloring proper subset prune and search pseudo-random number generator 33< 0 ::::::::::::::::::::::::::::::::: !.>--? ::::::::::::::::::::: !.>--? !"'J? :::::::::::::: :::::::::::::::::: K6* !"< :::::::::::::: :::::::::::::::::::::::::: ::::::::::::::::::::::::::::::: ::::::::::: ::::::::::::::::: K6* FNO K6* $K6* " * + & ::::::::::::::::::::::::::::::::::::: !.>--? $D ::::::::::: FY *) ! #/( !">.) * &$& ?4" > a $K6* !".D 9 simple merge simple path simulation theorem single-destination shortest-path problem :::::::::::::::::::::::: :::::::::::::::::::::::::: ::::::::::: ! * recursion tree recursive recursive data structure recursive language recursively enumerable language 12 :::::::::::::::::::: ::::::::::::::::::::::::::::::: " !"ZH :::::: 4- g " !"'7 reduced basis reduced digraph reduction reexive regular decomposition relation relational structure relative performance guarantee :::::::::: b g * !"'7 !"<-( 3'E :::::::::::::::::::::::::::::::::::: ( ? * C :::::::::::::::::::: ( ? * C :::::::::::::::::::::: ::::::::::::::::::::: ::::: :::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::: "K+ :::::::::::::::::::::::: :::::::::::::::::::::::::: ::::::::::::::::::: ::::::::::::::::::::::: $% :::::::: :::::::::::::::: :::::::::::::::: C TL - & !"ZH ">.) ">.) s.& !"R?% ::::::::::::::::::::::: ?J * C ::::::::::::::::::::::: ?J * C ::::: 6 ? $D ::::::::::::::::::::::::: 10 "H\ ">.) M :::::::::::::: C ">.) 3= ::::::::::::::::::::: P? 5 ">.) 3. ::::::::::::::::::: C - * ! * :::::::::::::::::::::::: b "(% :::::::::::: ::::::::::::::::: $( L( * :::::::::::::::::::: $% 86 - s P :::::::::::::::::: $D ::::::::::::::::::::::: t s :::::::::::::::::::::::::::::::::::: !"<-( ::::::::::::::::::::::: & ,* :::::::::::::::::::::::::::::::::: !". $D ::::::::::::::::::::: ::::::::: :::::::::::::::::::: $% ::::::::::::::::::::::: - B 6 ::::::::::::::::::::::::::::::: s $% :::::::::::::::::::::: :::::::::::::::::: s-t cut saturated edge selection sort self-loop separation theorem set set complement set dierence set intersection set union shared memory shell sort Shell sort Shor's algorithm shortest path shortest spanning tree Sierpinski triangle signature O'=V ::::::::::::::::::::::::::::::::::::: S ! "K+ $D 3! C 0 5 :::::::::::::::::::::::::::::: 1 !"K + rho -- ::::::::::::::::::::::: F'D 8+-* E ,A& * ::::::::::::::::::::::: Z? @ :::::::::::::::::::::::::::::::::::: :::::: :::: O 0 ::::::::::::::::::::::::: "< ! "< D :::::::::::::::::::::::::: b ,@ ! * R !" #) :::::::::::::::::::::::::::::::: F'D B 6 ::::::::::::::::::::::: :::::: * relaxation rescalable restricted universe sort rho-approximation algorithm Rice's method rough graph run time F'D 0 :::::::::::::::::::: ::::::::::::::::::::::::::::::::: ( $(.= 8+3% D ::::::::::::::::::::: ,G :::::::::::::: C :::::::::::::::::::::::::::::::: ! * :::::::::::::::::::::::::::::::::: C L( ! * qV , - :::::::::::::::::::::::::::::::: !"+ $A& B 6 ::::::::::::: gV ::::::::::::::::::::::: ::::::::::::::::::::: "?\g !(+ $ :::::::::::: K6* , * :::::::::::::::::::: single-source shortest-path problem :::::::::: 8+5.K6* , * b h * g !"'7 ::::::::::: K6* K6* D ::::::::::::::::: single-pair shortest-path problem singly linked list singularity analysis sink sink sort sinking sort skew symmetry slope selection solvable sorting algorithm source space-constructible function sparse graph sparse matrix sparsication square matrix square root stable stack stack tree star-shaped polygon start state state state machine state transition Steiner minimum tree Steiner point Steiner ratio Steiner tree Steiner vertex Stirling's approximation Stirling's formula stooge sort straight-line drawing $K6* $D + n'm (,K() tZ strictly decreasing strictly increasing strictly lower triangular matrix f !"'7 8+(.4 U tour tractable transducer transition transition function transitive transitive reduction traveling salesman traveling salesman problem :::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::: :::::::::::::::::::: m'm + f 0 P strictly upper triangular matrix ($O= u) 86 ::::::::::::::::::::: :::::::::::::::::::::::: :::::::::::: m'm N f 0 86 @ string strongly connected graph subadditive ergodic theorem (! 86 ) :::::::::::::: !* c ::::::::::::::::::::::::::::::::::::: :::::::: 6 ! ? ::::::::::: subgraph subgraph isomorphism subset sux automaton superset supersink supersource symmetric symmetric set dierence symmetrically linked list :::::::::::::::::: D , D * :::::::::::::::: ." ::::::::::::::::::::: :::::::::::::::::: ::::::::::::::::: G ::::::::::::::::: :::::: !O e "?\ $ " 2 * ::::::::::::::::::::::::::::: @ d :::::::::::::::::::::::::::::: , - ::: ">.) , - 3= :::: , - !(+ $ tail tail recursion temporal logic terminal text theta three-dimensional three-way merge sort time/space complexity top-down radix sort top-down tree automaton ::::::::::::::::::::::::::::::::::::::::: C :::::::::::::::::::: U (* ;< :::::::::::::::::::::::::::::::::: ::::::::: ::::: @ 8+(" 8+(" ::::::::::: :::::::: ::::::::::::::::::::: 8+(.4 :::: 8+(.4 , * 8+(.4 !"'7 :::::::::::::: ::: $A&2 B 6 " ::::: top sort topological order topological sort total function total order totally decidable problem totally undecidable problem $D (g ! ! (D ::::::::::::::: ::::::::::::::::: :::: ::::::::::::: s.& :::::::::::::::::::::: @& $% :::::::::::::::::::::::::: (@& !">.)) ,A& (K(3% 11 C C C [ + C [ + * ::::::::::::::::::::::::: @& ::::::::::::::::::::::::::: [ + * ::::::::::::::: s.& 2 * "R?%/,* 6S+ + " N D , c ::::::::::::::::::::: $D (g 0 c !O " e + " N * $D (g 6S+ ::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::: E !"'7 :::::::::::::::::::::::: "(+ ::::::::::::::::::::::::::::::::::::::: E @ 1 e $K6* D/ :::::::::::::::::::::: :::::::::::::::::::::: ::::::::::::::::: gV d T "?\ !(+ $ c ::::::::::::::::::::::: ">.) * dc ::::::::::::::::::::::::::::: P ::::::::::::::::::::::: ">.) * !(+ , :::::::::::::::::::::::::::: @ B 6 * B 6 * L :::::::::::::::: B 6 " ::::::: ::::::::::::::::::::::::::::::: C m'm !( ::::::::::::::: ::::::::: :::::::::::::::::::::::::::::: 6 ! ? :::::::::::::::::::::::: unary function uncomputable function uncomputable problem undecidable undecidable language undecidable problem undirected graph uniform circuit complexity uniform circuit family uniform matrix union union of automata universal state universal Turing machine universe unsolvable " f H B 6 . O.& * g6 !"ZH 6 ! ? !"'7 travelling salesman tree automaton tree sort triangle inequality triconnected graph trinary function Turing machine Turing reduction Turing transducer two-dimensional two-way linked list two-way list two-way merge sort !OJ f ::::::::::::::::: (A :::::::::::::::::::::::::::::::: #( f ::::::::::::::::::: C 3 @ 3 C f !"'7 8+.4 U visibility map visible Viterbi algorithm ::::::::::::::::::::::: ::::::::::::::::::::::::::::::::: ::::::::::::::: unsolvable problem unsorted list upper triangular matrix !"K-( ::::::::::: 3H ::::::::::::::::::::::: W walk weak-heap sort weighted graph weighted, directed graph worst-case worst-case cost IO= * :::::::::::::::::::: ::: vehicle routing problem Veitch diagram Venn diagram vertex vertex coloring vertex connectivity vertex cover vertex set vertical visibility map vertices $K6 C , * B 6 "' !"'7 ` .( , .( :::::::::::::::::::::::::::::::::::: $% ::::::::::::::::: $% !" # ::::::::::::::::::::::::::::::: :: :::::::::::::::::::::::: ::::::::::::::: :::::::::::::::::::::::: X xor m'mN 0 :::::::::::::::::::::: , * $A& B 6 ::::::::::::::::::::::::: ::::::::::::: :::::::: C( $ V ::::::::::::::::::::::::::::::::::::: :::::::::::: (K(3% !"'7 ::::::::::::::::::::: ! 4E( ! :::::::: b ! #/( b !. b G+ b !">.) !.> !"K-( ::::::::::::::::::::::::::::::::: 12 b b
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