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An optimal algorithm to solve the allpairs shortest paths on unweighted interval graphs
 Networks
, 1992
"... We present an O(n2) timeoptimal algorithm for solving the unweighted allpair shortest path problem on interval graphs, an important subclass of perfect graphs. An interesting structure called the neighborhood tree is studied and used in the algorithm. This tree is formed by identifying the success ..."
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Cited by 7 (0 self)
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We present an O(n2) timeoptimal algorithm for solving the unweighted allpair shortest path problem on interval graphs, an important subclass of perfect graphs. An interesting structure called the neighborhood tree is studied and used in the algorithm. This tree is formed by identifying
Dynamic Approximate AllPairs Shortest Paths in Undirected Graphs
"... Abstract We obtain three new dynamic algorithms for the approximate allpairs shortest paths problem in unweighted undirected graphs: 1. For any fixed " ? 0, a decremental algorithm withan expected total running time of ~O(mn), where m is the number of edges and n is the number of vertice ..."
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Abstract We obtain three new dynamic algorithms for the approximate allpairs shortest paths problem in unweighted undirected graphs: 1. For any fixed " ? 0, a decremental algorithm withan expected total running time of ~O(mn), where m is the number of edges and n is the number of ver
AllPairs Shortest Paths with a Sublinear Additive Error
"... We show that for every 0 ≤ p ≤ 1 there is an O(n 2.575−p/(7.4−2.3p) ) time algorithm that given a directed graph with small positive integer weights, estimates the length of the shortest path between every pair of vertices u, v in the graph to within an additive error δ p (u, v), where δ(u, v) is th ..."
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Cited by 1 (0 self)
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We show that for every 0 ≤ p ≤ 1 there is an O(n 2.575−p/(7.4−2.3p) ) time algorithm that given a directed graph with small positive integer weights, estimates the length of the shortest path between every pair of vertices u, v in the graph to within an additive error δ p (u, v), where δ(u, v
Faster Algorithms for Approximate Distance Oracles and AllPairs Small StretchPaths
"... ffi(u, v) < = ^ffi(u, v) < = t * ffi(u, v). The most efficient algorithms known for computing small stretch distances in Gare the approximate distance oracles of [16] and the three algorithms in [9] to compute allpairs stretch t distancesfor t = 2, 7/3, and 3. We present faster algorithms fo ..."
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israther high. Here we present an O(n2 log n) algorithm toconstruct such a data structure of size O(kn1+1/k) for allintegers k> = 2. Our query answering time is O(k) for k>2 and \Theta (log n) for k = 2. We use a new generic scheme forallpairs approximate shortest paths for these results
AllPairs Bottleneck Paths in Vertex Weighted Graphs
 In Proc. of SODA, 978–985
, 2007
"... Let G = (V, E, w) be a directed graph, where w: V → R is an arbitrary weight function defined on its vertices. The bottleneck weight, or the capacity, of a path is the smallest weight of a vertex on the path. For two vertices u, v the bottleneck weight, or the capacity, from u to v, denoted c(u, v), ..."
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Cited by 9 (1 self)
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), is the maximum bottleneck weight of a path from u to v. In the AllPairs Bottleneck Paths (APBP) problem we have to find the bottleneck weights for all ordered pairs of vertices. Our main result is an O(n 2.575) time algorithm for the APBP problem. The exponent is derived from the exponent of fast matrix
Faster Language Edit Distance, Connection to Allpairs Shortest Paths and Related Problems
"... Given a context free language L(G) over alphabet Σ and a string s ∈ Σ∗, the language edit distance problem seeks the minimum number of edits (insertions, deletions and substitutions) required to convert s into a valid member of L(G). The wellknown dynamic programming algorithm solves this problem i ..."
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tiplicative approximation factor of (1 + ) with high probability, where ω is the exponent of ordinary matrix multiplication of n dimensional square matrices. It also computes the edit script. We further solve the local alignment problem; for all substrings of s, we can estimate their language edit distance
Allpairs nearly 2approximate shortestpaths in O(n² polylog n) time
 IN PROCEEDINGS OF 22ND ANNUAL SYMPOSIUM ON THEORETICAL ASPECT OF COMPUTER SCIENCE, VOLUME 3404 OF LNCS
, 2005
"... Let G(V, E) be an unweighted undirected graph on V = n vertices. Let δ(u, v) denote the shortest distance between vertices u, v ∈ V. An algorithm is said to compute allpairs tapproximate shortestpaths/distances, for some t ≥ 1, if for each pair of vertices u, v ∈ V, the path/distance reported ..."
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Cited by 13 (6 self)
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by the algorithm is not longer/greater than t · δ(u, v). This paper presents two randomized algorithms for computing allpairs nearly 2approximate distances. The first algorithm takes expected O(m 2/3 n log n+n²) time, and for any u, v ∈ V reports distance no greater than 2δ(u, v) + 1. Our second algorithm
On the exponent of the all pairs shortest path problem
"... The upper bound on the exponent, ω, of matrix multiplication over a ring that was three in 1968 has decreased several times and since 1986 it has been 2.376. On the other hand, the exponent of the algorithms known for the all pairs shortest path problem has stayed at three all these years even for t ..."
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Cited by 84 (2 self)
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The upper bound on the exponent, ω, of matrix multiplication over a ring that was three in 1968 has decreased several times and since 1986 it has been 2.376. On the other hand, the exponent of the algorithms known for the all pairs shortest path problem has stayed at three all these years even
An O(n 3 log log n / log n) Time Algorithm for the AllPairs Shortest Path Problem
, 2004
"... We design a faster algorithm for the allpairs shortest path problem under the conventional RAM model, based on distance matrix multiplication (DMM). Specifically we improve the best known time complexity of O(n 3 (log log n) 2 / log n) to O(n 3 log log n / log n). As an application, we show the km ..."
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Cited by 6 (2 self)
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We design a faster algorithm for the allpairs shortest path problem under the conventional RAM model, based on distance matrix multiplication (DMM). Specifically we improve the best known time complexity of O(n 3 (log log n) 2 / log n) to O(n 3 log log n / log n). As an application, we show the k
AllPairs Bottleneck Paths For General Graphs in Truly SubCubic Time
 STOC'07
, 2007
"... In the allpairs bottleneck paths (APBP) problem (a.k.a. allpairs maximum capacity paths), one is given a directed graph with real nonnegative capacities on its edges and is asked to determine, for all pairs of vertices s and t, the capacity of a single path for which a maximum amount of flow can b ..."
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Cited by 12 (6 self)
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,min)product of two arbitrary matrices over R ∪ {∞, −∞} in O(n 2+ω/3) ≤ O(n 2.792) time, where n is the number of vertices and ω is the exponent for matrix multiplication over rings. Using this procedure, an explicit maximum bottleneck path for any pair of nodes can be extracted in time linear in the length
Results 11  20
of
650