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16
Exact and Approximate Distances in Graphs  a survey
 In ESA
, 2001
"... We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different settings and models and try to identify some remaining open problems. ..."
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Cited by 57 (0 self)
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We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different settings and models and try to identify some remaining open problems.
LinearTime PointerMachine Algorithms for Least Common Ancestors, MST Verification, and Dominators
 IN PROCEEDINGS OF THE THIRTIETH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1998
"... We present two new data structure toolsdisjoint set union with bottomup linking, and pointerbased radix sortand combine them with bottomlevel microtrees to devise the first lineartime pointermachine algorithms for offline least common ancestors, minimum spanning tree (MST) verification, ..."
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Cited by 27 (4 self)
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We present two new data structure toolsdisjoint set union with bottomup linking, and pointerbased radix sortand combine them with bottomlevel microtrees to devise the first lineartime pointermachine algorithms for offline least common ancestors, minimum spanning tree (MST) verification, randomized MST construction, and computing dominators in a flowgraph.
A New Approach to AllPairs Shortest Paths on RealWeighted Graphs
 Theoretical Computer Science
, 2003
"... We present a new allpairs shortest path algorithm that works with realweighted graphs in the traditional comparisonaddition model. It runs in O(mn+n time, improving on the longstanding bound of O(mn + n log n) derived from an implementation of Dijkstra's algorithm with Fibonacci heaps. Her ..."
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Cited by 26 (2 self)
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We present a new allpairs shortest path algorithm that works with realweighted graphs in the traditional comparisonaddition model. It runs in O(mn+n time, improving on the longstanding bound of O(mn + n log n) derived from an implementation of Dijkstra's algorithm with Fibonacci heaps. Here m and n are the number of edges and vertices, respectively.
Experimental Evaluation of a New Shortest Path Algorithm (Extended Abstract)
, 2002
"... We evaluate the practical eciency of a new shortest path algorithm for undirected graphs which was developed by the rst two authors. This algorithm works on the fundamental comparisonaddition model. Theoretically, this new algorithm outperforms Dijkstra's algorithm on sparse graphs for the al ..."
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Cited by 13 (4 self)
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We evaluate the practical eciency of a new shortest path algorithm for undirected graphs which was developed by the rst two authors. This algorithm works on the fundamental comparisonaddition model. Theoretically, this new algorithm outperforms Dijkstra's algorithm on sparse graphs for the allpairs shortest path problem, and more generally, for the problem of computing singlesource shortest paths from !(1) different sources. Our extensive experimental analysis demonstrates that this is also the case in practice. We present results which show the new algorithm to run faster than Dijkstra's on a variety of sparse graphs when the number of vertices ranges from a few thousand to a few million, and when computing singlesource shortest paths from as few as three different sources.
A shortest path algorithm for realweighted undirected graphs
 in 13th ACMSIAM Symp. on Discrete Algs
, 1985
"... Abstract. We present a new scheme for computing shortest paths on realweighted undirected graphs in the fundamental comparisonaddition model. In an efficient preprocessing phase our algorithm creates a linearsize structure that facilitates singlesource shortest path computations in O(m log α) ti ..."
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Cited by 12 (3 self)
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Abstract. We present a new scheme for computing shortest paths on realweighted undirected graphs in the fundamental comparisonaddition model. In an efficient preprocessing phase our algorithm creates a linearsize structure that facilitates singlesource shortest path computations in O(m log α) time, where α = α(m, n) is the very slowly growing inverseAckermann function, m the number of edges, and n the number of vertices. As special cases our algorithm implies new bounds on both the allpairs and singlesource shortest paths problems. We solve the allpairs problem in O(mnlog α(m, n)) time and, if the ratio between the maximum and minimum edge lengths is bounded by n (log n)O(1) , we can solve the singlesource problem in O(m + nlog log n) time. Both these results are theoretical improvements over Dijkstra’s algorithm, which was the previous best for real weighted undirected graphs. Our algorithm takes the hierarchybased approach invented by Thorup. Key words. singlesource shortest paths, allpairs shortest paths, undirected graphs, Dijkstra’s
I/Oefficient undirected shortest paths
 In Proc. 11th Annual European Symposium on Algorithms, volume 2832 of LNCS
, 2003
"... Abstract. We show how to compute singlesource shortest paths in undirected graphs with nonnegative edge lengths in O ( p nm/B log n + MST (n, m)) I/Os, where n is the number of vertices, m is the number of edges, B is the disk block size, and MST (n, m) is the I/Ocost of computing a minimum spann ..."
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Cited by 11 (4 self)
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Abstract. We show how to compute singlesource shortest paths in undirected graphs with nonnegative edge lengths in O ( p nm/B log n + MST (n, m)) I/Os, where n is the number of vertices, m is the number of edges, B is the disk block size, and MST (n, m) is the I/Ocost of computing a minimum spanning tree. For sparse graphs, the new algorithm performs O((n / √ B) log n) I/Os. This result removes our previous algorithm’s dependence on the edge lengths in the graph. 1
A Faster Allpairs Shortest Path Algorithm for Realweighted Sparse Graphs
 In Proc. 29th Int'l Colloq. on Automata, Languages, and Programming (ICALP'02), LNCS
, 2002
"... We present a faster allpairs shortest paths algorithm for arbitrary realweighted directed graphs. ..."
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Cited by 10 (3 self)
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We present a faster allpairs shortest paths algorithm for arbitrary realweighted directed graphs.
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 in a ..."
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Cited by 6 (5 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 inherent in approaches based on Dijkstra's algorithm, and for graphs with O(n) edges our algorithm is within a tiny O(log (n; n)) factor of optimal. Our algorithm can be implemented to run in polynomial time (granted, a large polynomial). We leave open the problem of providing an efficient implementation.
Advanced Shortest Paths Algorithms on a MassivelyMultithreaded Architecture
"... We present a study of multithreaded implementations of Thorup’s algorithm for solving the Single Source Shortest Path (SSSP) problem for undirected graphs. Our implementations leverage the fledgling MultiThreaded Graph Library (MTGL) to perform operations such as finding connected components and ext ..."
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Cited by 3 (0 self)
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We present a study of multithreaded implementations of Thorup’s algorithm for solving the Single Source Shortest Path (SSSP) problem for undirected graphs. Our implementations leverage the fledgling MultiThreaded Graph Library (MTGL) to perform operations such as finding connected components and extracting induced subgraphs. To achieve good parallel performance from this algorithm, we deviate from several theoretically optimal algorithmic steps. In this paper, we present simplifications that perform better in practice, and we describe details of the multithreaded implementation that were necessary for scalability. We study synthetic graphs that model unstructured networks, such as social networks and economic transaction networks. Most of the recent progress in shortest path algorithms relies on structure that these networks do not have. In this work, we take a step back and explore the synergy between an elegant theoretical algorithm and an elegant computer architecture. Finally, we conclude with a prediction that this work will become relevant to shortest path computation on structured networks. 1.
Improved Distance Oracles for Avoiding LinkFailure
 In Proc. of the 13th International Symposium on Algorithms and Computation (ISAAC’02
, 2002
"... We consider the problem of preprocessing an edgeweighted directed graph to answer queries that ask for the shortest path from any given vertex to another avoiding a failed link. We present two algorithms that improve on earlier results for this problem. Our first algorithm, which is a modification ..."
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Cited by 3 (2 self)
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We consider the problem of preprocessing an edgeweighted directed graph to answer queries that ask for the shortest path from any given vertex to another avoiding a failed link. We present two algorithms that improve on earlier results for this problem. Our first algorithm, which is a modification of an earlier method, improves the query time to a constant while maintaining the earlier bounds for preprocessing time and space. Our second result is a new algorithm whose preprocessing time is considerably faster than earlier results and whose query time and space are worse by no more than a logarithmic factor.