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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 16 (4 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
Parallel Shortest Path Algorithms for Solving . . .
, 2006
"... We present an experimental study of the single source shortest path problem with nonnegative edge weights (NSSP) on largescale graphs using the ∆stepping parallel algorithm. We report performance results on the Cray MTA2, a multithreaded parallel computer. The MTA2 is a highend shared memory s ..."
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Cited by 15 (3 self)
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We present an experimental study of the single source shortest path problem with nonnegative edge weights (NSSP) on largescale graphs using the ∆stepping parallel algorithm. We report performance results on the Cray MTA2, a multithreaded parallel computer. The MTA2 is a highend shared memory system offering two unique features that aid the efficient parallel implementation of irregular algorithms: the ability to exploit finegrained parallelism, and lowoverhead synchronization primitives. Our implementation exhibits remarkable parallel speedup when compared with competitive sequential algorithms, for lowdiameter sparse graphs. For instance, ∆stepping on a directed scalefree graph of 100 million vertices and 1 billion edges takes less than ten seconds on 40 processors of the MTA2, with a relative speedup of close to 30. To our knowledge, these are the first performance results of a shortest path problem on realistic graph instances in the order of billions of vertices and edges.
An experimental study of a parallel shortest path algorithm for solving largescale graph instances
 Ninth Workshop on Algorithm Engineering and Experiments (ALENEX 2007)
, 2007
"... We present an experimental study of the single source shortest path problem with nonnegative edge weights (NSSP) on largescale graphs using the $\Delta$stepping parallel algorithm. We report performance results on the Cray MTA2, a multithreaded parallel computer. The MTA2 is a highend shared m ..."
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Cited by 12 (3 self)
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We present an experimental study of the single source shortest path problem with nonnegative edge weights (NSSP) on largescale graphs using the $\Delta$stepping parallel algorithm. We report performance results on the Cray MTA2, a multithreaded parallel computer. The MTA2 is a highend shared memory system offering two unique features that aid the efficient parallel implementation of irregular algorithms: the ability to exploit finegrained parallelism, and lowoverhead synchronization primitives. Our implementation exhibits remarkable parallel speedup when compared with competitive sequential algorithms, for lowdiameter sparse graphs. For instance, $\Delta$stepping on a directed scalefree graph of 100 million vertices and 1 billion edges takes less than ten seconds on 40 processors of the MTA2, with a relative speedup of close to 30. To our knowledge, these are the first performance results of a shortest path problem on realistic graph instances in the order of billions of vertices and edges.
A robot path planning algorithm based on renormalized measure of probabilistic regular languages
 Int. J. Control
, 2009
"... probabilistic regular languages ..."
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Barcelona Aarhus Barcelona
, 2002
"... This is the second annual progress report for the ALCOMFT project, supported by the European ..."
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This is the second annual progress report for the ALCOMFT project, supported by the European
Design and Analysis of Sequential . . .
, 2002
"... We study the performance of algorithms for the SingleSource ShortestPaths (SSSP) problem on graphs withÒnodes andÑedges with nonnegative random weights. All previously known SSSP algorithms for directed graphs required superlinear time. We give the first SSSP algorithms that provably achieve line ..."
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We study the performance of algorithms for the SingleSource ShortestPaths (SSSP) problem on graphs withÒnodes andÑedges with nonnegative random weights. All previously known SSSP algorithms for directed graphs required superlinear time. We give the first SSSP algorithms that provably achieve linearÇÒÑaveragecase execution time on arbitrary directed graphs with random edge weights. For independent edge weights, the lineartime bound holds with high probability, too. Additionally, our result implies improved averagecase bounds for the AllPairs ShortestPaths (APSP) problem on sparse graphs, and it yields the first theoretical averagecase analysis for the “Approximate Bucket Implementation” of Dijkstra’s SSSP algorithm (ABI–Dijkstra). Furthermore, we give constructive proofs for the existence of graph classes with random edge weights on which ABI–Dijkstra and several other wellknown SSSP algorithms require superlinear averagecase time. Besides the classical sequential (single processor) model of computation we also consider parallel computing: we give the currently fastest averagecase linearwork parallel SSSP algorithms for large graph classes with random edge weights, e.g., sparse random graphs and graphs modeling the WWW, telephone calls or social networks.
Design and Analysis of Sequential and Parallel . . .
, 2002
"... We study the performance of algorithms for the SingleSource ShortestPaths (SSSP) problem on graphs with nodes and edges with nonnegative random weights. All previously known SSSP algorithms for directed graphs required superlinear time. We give the first SSSP algorithms that provably achieve lin ..."
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We study the performance of algorithms for the SingleSource ShortestPaths (SSSP) problem on graphs with nodes and edges with nonnegative random weights. All previously known SSSP algorithms for directed graphs required superlinear time. We give the first SSSP algorithms that provably achieve linear averagecase execution time on arbitrary directed graphs with random edge weights. For independent edge weights, the lineartime bound holds with high probability, too. Additionally, our result implies improved averagecase bounds for the AllPairs ShortestPaths (APSP) problem on sparse graphs, and it yields the first theoretical averagecase analysis for the “Approximate Bucket Implementation” of Dijkstra’s SSSP algorithm (ABI–Dijkstra). Furthermore, we give constructive proofs for the existence of graph classes with random edge weights on which ABI–Dijkstra and several other wellknown SSSP algorithms require superlinear averagecase time. Besides the classical sequential (single processor) model of computation we also consider parallel computing: we give the currently fastest averagecase linearwork parallel SSSP algorithms for large graph classes with random edge weights, e.g., sparse random graphs and graphs modeling the WWW, telephone calls or social networks.