Results 1  10
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127,897
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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multiplication. Our algorithm is the first subcubic algorithm for this problem. Unlike the subcubic algorithm for the allpairs shortest paths (APSP) problem, that only applies to bounded (or relatively small) integer edge or vertex weights, the algorithm presented for APBP problem works for arbitrary large
Parallel FPGAbased AllPairs ShortestPaths in a Directed Graph
 IN PROCEEDINGS OF THE 20TH IEEE INTERNATIONAL PARALLEL AND DISTRIBUTED PROCESSING SYMPOSIUM
, 2006
"... With rapid advances in VLSI technology, Field Programmable Gate Arrays (FPGAs) are receiving the attention of the Parallel and High Performance Computing community. In this paper, we propose a highly parallel FPGA design for the FloydWarshall algorithm to solve the allpairs shortestpaths problem i ..."
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Cited by 14 (3 self)
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With rapid advances in VLSI technology, Field Programmable Gate Arrays (FPGAs) are receiving the attention of the Parallel and High Performance Computing community. In this paper, we propose a highly parallel FPGA design for the FloydWarshall algorithm to solve the allpairs shortestpaths problem
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
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
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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computational rule, the sumproduct algorithm operates in factor graphs to computeeither exactly or approximatelyvarious marginal functions by distributed messagepassing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 627 (44 self)
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as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar
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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/Os for allpairs shortest paths and diameter in unweighted undirected graphs. For weighted undirected graphs we present a cacheaware APSP algorithm that performs O(V * (q V EB + EB log VB)) I/Os. We also present efficient cacheaware algorithms that find paths between all pairs of vertices in anunweighted
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
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
Results 1  10
of
127,897