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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
FASTER ALGORITHMS FOR ALLPAIRS APPROXIMATE SHORTEST PATHS IN UNDIRECTED GRAPHS
, 2006
"... Let G = (V, E) be a weighted undirected graph having nonnegative edge weights. An estimate ˆ δ(u, v) of the actual distance δ(u, v) between u, v ∈ V is said to be of stretch t iff δ(u, v) ≤ ˆ δ(u, v) ≤ t · δ(u, v). Computing allpairs small stretch distances efficiently (both in terms of time ..."
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Cited by 8 (2 self)
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and space) is a wellstudied problem in graph algorithms. We present a simple, novel and generic scheme for allpairs approximate shortest paths. Using this scheme and some new ideas and tools, we design faster algorithms for allpairs tstretch distances for a whole range of stretch t, and also answer
ExternalMemory Exact and Approximate AllPairs ShortestPaths in Undirected Graphs
, 2004
"... We present several new externalmemory algorithms for finding allpairs shortest paths in a Vnode, Eedge undirected graph. For allpairs shortest paths and diameter in unweighted undirected graphs we present cacheoblivious algorithnls with O(V. ~ log. ~ ~) I/Os, where B is the blocksize and M is ..."
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Cited by 6 (1 self)
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We present several new externalmemory algorithms for finding allpairs shortest paths in a Vnode, Eedge undirected graph. For allpairs shortest paths and diameter in unweighted undirected graphs we present cacheoblivious algorithnls with O(V. ~ log. ~ ~) I/Os, where B is the blocksize and M
ExternalMemory Exact and Approximate AllPairs ShortestPaths in Undirected Graphs *
, 2004
"... Abstract We present several new externalmemory algorithms for finding allpairs shortest paths in a Vnode, Eedge undirected graph. Our results include the following, where B is the blocksize and Mis the size of internal memory. We present cacheoblivious algorithms with O( V * EB log MB EB) I/Os ..."
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Abstract We present several new externalmemory algorithms for finding allpairs shortest paths in a Vnode, Eedge undirected graph. Our results include the following, where B is the blocksize and Mis the size of internal memory. We present cacheoblivious algorithms with O( V * EB log MB EB) I
Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
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Cited by 401 (2 self)
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We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest
AllPairs Shortest Paths for Unweighted Undirected Graphs in o(mn) Time
 Proc. ACMSIAM Symposium on Discrete Algorithms (SODA
, 2006
"... Abstract We revisit the allpairsshortestpaths problem for an unweighted undirected graph with n vertices and m edges. We present new algorithms with the following running times: O(mn = log n) if m? n log ..."
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Cited by 22 (1 self)
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Abstract We revisit the allpairsshortestpaths problem for an unweighted undirected graph with n vertices and m edges. We present new algorithms with the following running times: O(mn = log n) if m? n log
Finding the Hidden Path: Time Bounds for AllPairs Shortest Paths
, 1993
"... We investigate the allpairs shortest paths problem in weighted graphs. We present an algorithmthe Hidden Paths Algorithmthat finds these paths in time O(m* n+n² log n), where m is the number of edges participating in shortest paths. Our algorithm is a practical substitute for Dijkstra&ap ..."
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Cited by 76 (0 self)
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We investigate the allpairs shortest paths problem in weighted graphs. We present an algorithmthe Hidden Paths Algorithmthat finds these paths in time O(m* n+n² log n), where m is the number of edges participating in shortest paths. Our algorithm is a practical substitute for Dijkstra
Average update times for fullydynamic allpairs shortest paths
 Proceedings of the 19th International Symposium on Algorithms and Computation (ISAAC 2008), Gold Coast, Australia, 2008, LNCS 5369
"... Abstract We study the fullydynamic all pairs shortest path problem for graphs with arbitrary nonnegative edge weights. It is known for digraphs that an update of the distance matrix costs Õ(n2.75) 1 worstcase time [Thorup, STOC ’05] and Õ(n2) amortized time [Demetrescu and Italiano, J.ACM ’04] wh ..."
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Cited by 2 (0 self)
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Abstract We study the fullydynamic all pairs shortest path problem for graphs with arbitrary nonnegative edge weights. It is known for digraphs that an update of the distance matrix costs Õ(n2.75) 1 worstcase time [Thorup, STOC ’05] and Õ(n2) amortized time [Demetrescu and Italiano, J.ACM ’04
On the ComparisonAddition Complexity of AllPairs Shortest Paths
 In Proc. 13th Int'l Symp. on Algorithms and Computation (ISAAC'02
, 2002
"... We present an allpairs shortest path algorithm for arbitrary graphs that performs O(mn log (m; n)) comparison and addition operations, where m and n are the number of edges and vertices, resp., and is Tarjan's inverseAckermann function. Our algorithm eliminates the sorting bottleneck inherent ..."
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Cited by 10 (6 self)
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We present an allpairs shortest path algorithm for arbitrary graphs that performs O(mn log (m; n)) comparison and addition operations, where m and n are the number of edges and vertices, resp., and is Tarjan's inverseAckermann function. Our algorithm eliminates the sorting bottleneck
Results 1  10
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234,040