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14
Distributed LTL Model Checking Based on Negative Cycle Detection
, 2001
"... This paper addresses the state explosion problem in automata based LTL model checking. To deal with large space requirements we turn to use a distributed approach. All the known methods for automata based model checking are based on depth first traversal of the state space which is difficult to para ..."
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Cited by 29 (13 self)
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This paper addresses the state explosion problem in automata based LTL model checking. To deal with large space requirements we turn to use a distributed approach. All the known methods for automata based model checking are based on depth first traversal of the state space which is difficult to parallelise as the ordering in which vertices are visited plays an important role. We come up with entirely different approach which is dependent on locating cycles with negative length in a directed graph with real number length of edges. Our method allows reasonable distribution and the experimental results confirm its usefulness for distributed model checking.
A Parallelization of Dijkstra's Shortest Path Algorithm
 IN PROC. 23RD MFCS'98, LECTURE NOTES IN COMPUTER SCIENCE
, 1998
"... The single source shortest path (SSSP) problem lacks parallel solutions which are fast and simultaneously workefficient. We propose simple criteria which divide Dijkstra's sequential SSSP algorithm into a number of phases, such that the operations within a phase can be done in parallel. We give a P ..."
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Cited by 27 (6 self)
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The single source shortest path (SSSP) problem lacks parallel solutions which are fast and simultaneously workefficient. We propose simple criteria which divide Dijkstra's sequential SSSP algorithm into a number of phases, such that the operations within a phase can be done in parallel. We give a PRAM algorithm based on these criteria and analyze its performance on random digraphs with random edge weights uniformly distributed in [0, 1]. We use
A Parallel Priority Queue with Constant Time Operations
 JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
, 1998
"... We present a parallel priority queue that supports the following operations in constant time: parallel insertion of a sequence of elements ordered according to key, parallel decrease key for a sequence of elements ordered according to key, deletion of the minimum key element, as well as deletion ..."
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Cited by 15 (1 self)
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We present a parallel priority queue that supports the following operations in constant time: parallel insertion of a sequence of elements ordered according to key, parallel decrease key for a sequence of elements ordered according to key, deletion of the minimum key element, as well as deletion of an arbitrary element. Our data structure is the first to support multi insertion and multi decrease key in constant time. The priority queue can be implemented on the EREW PRAM, and can perform any sequence of n operations in O(n) time and O(m log n) work, m being the total number of keys inserted and/or updated. A main application is a parallel implementation of Dijkstra's algorithm for the singlesource shortest path problem, which runs in O(n) time and O(m log n) work on a CREW PRAM on graphs with n vertices and m edges. This is a logarithmic factor improvement in the running time compared with previous approaches.
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
Parallel Shortest Path for Arbitrary Graphs
 In EUROPAR: Parallel Processing, 6th International EUROPAR Conference. LNCS
, 2000
"... . In spite of intensive research, no workecient parallel algorithm for the single source shortest path problem is known which works in sublinear time for arbitrary directed graphs with nonnegative edge weights. We present an algorithm that improves this situation for graphs where the ratio dc= ..."
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Cited by 11 (4 self)
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. In spite of intensive research, no workecient parallel algorithm for the single source shortest path problem is known which works in sublinear time for arbitrary directed graphs with nonnegative edge weights. We present an algorithm that improves this situation for graphs where the ratio dc= between the maximum weight of a shortest path dc and a \safe step width" is not too large. We show how such a step width can be found eciently and give several graph classes which meet the above condition, such that our parallel shortest path algorithm runs in sublinear time and uses linear work. The new algorithm is even faster than a previous one which only works for random graphs with random edge weights [10]. On those graphs our new approach is faster by a factor of (log n= log log n) and achieves an expected time bound of O(log 2 n) using linear work. 1 Introduction The single source shortest path problem (SSSP) is a fundamental and wellstudied combinatorial optimizati...
Distributed shortest path for directed graphs with negative edge lengths
, 2001
"... w\Delta\Theta\Xi\Pi\Sigma\Upsilon\Phi\Omega fffiflffiij`'ae/!"#$%&'()+,./012345!yA ..."
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Cited by 4 (3 self)
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How to Employ Reverse Search in Distributed Single Source Shortest Paths
, 2001
"... A distributed algorithm for the single source shortest path problem for directed graphs with arbitrary edge lengths is proposed. The new algorithm is based on relaxations and uses reverse search for inspecting edges and thus avoids using any additional data structures. At the same time the algorithm ..."
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Cited by 2 (2 self)
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A distributed algorithm for the single source shortest path problem for directed graphs with arbitrary edge lengths is proposed. The new algorithm is based on relaxations and uses reverse search for inspecting edges and thus avoids using any additional data structures. At the same time the algorithm uses a novel way to recognize a reachable negativelength cycle in the graph which facilitates the scalability of the algorithm.
Evaluation of shortest path query algorithm in spatial databases. a MMath Thesis presented to the
, 2003
"... I hereby declare that I am the sloe authour of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Many variations of algorithms for finding the shortest p ..."
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Cited by 1 (0 self)
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I hereby declare that I am the sloe authour of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Many variations of algorithms for finding the shortest path in a large graph have been introduced recently due to the needs of applications like the Geographic Information System (GIS) or Intelligent Transportation System (ITS). The primary subjects of those algorithms are materialization and hierarchical path views. Some studies focus on the materialization and sacrifice the precomputational costs and storage costs for faster computation of a query. Other studies focus on the shortestpath algorithm, which has less precomputation and storage but takes more time to compute the shortest path. The main objective of this thesis is to accelerate the computation time for the shortestpath queries while keeping the degree of materialization as low as possible. This thesis explores two different categories: 1) the reduction of the I/Ocosts for multiple queries, and 2) the reduction of search spaces in a graph. The thesis proposes
Parallel Algorithms for Detection of Negative Cycles
, 2003
"... Several new parallel algorithms for the single source shortest paths and for the negative cycle detection problems on directed graphs with real edge weights and given by adjacency list are developed, analysed, and experimentally compared. The algorithms are to be performed on clusters of worksta ..."
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Cited by 1 (0 self)
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Several new parallel algorithms for the single source shortest paths and for the negative cycle detection problems on directed graphs with real edge weights and given by adjacency list are developed, analysed, and experimentally compared. The algorithms are to be performed on clusters of workstations that communicate via a message passing mechanism.