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12
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 34 (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.
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 16 (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.
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 14 (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.
Buckets strike back: Improved Parallel ShortestPaths
 Proc. 16th Intl. Par. Distr. Process. Symp. (IPDPS
, 2002
"... We study the averagecase complexity of the parallel singlesource shortestpath (SSSP) problem, assuming arbitrary directed graphs with n nodes, m edges, and independent random edge weights uniformly distributed in [0; 1]. We provide a new bucketbased parallel SSSP algorithm that runs in T = O(log ..."
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Cited by 7 (2 self)
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We study the averagecase complexity of the parallel singlesource shortestpath (SSSP) problem, assuming arbitrary directed graphs with n nodes, m edges, and independent random edge weights uniformly distributed in [0; 1]. We provide a new bucketbased parallel SSSP algorithm that runs in T = O(log 2 n min i f2 i L + jV i jg) averagecase time using O(n+m+T ) work on a PRAM where L denotes the maximum shortestpath weight and jV i j is the number of graph vertices with indegree at least 2 i . All previous algorithms either required more time or more work. The minimum performance gain is a logarithmic factor improvement; on certain graph classes, accelerations by factors of more than n 0:4 can be achieved. The algorithm allows adaptation to distributed memory machines, too.
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 5 (3 self)
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Deterministic multicore parallel routing for FPGAs
 In IEEE FPT
, 2010
"... Abstract—We consider coarse and finegrained techniques for parallel FPGA routing on modern multicore processors. In the coarsegrained approach, sets of design signals are assigned to different processor cores and routed concurrently. Communication between cores is through the MPI (message passin ..."
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Cited by 3 (2 self)
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Abstract—We consider coarse and finegrained techniques for parallel FPGA routing on modern multicore processors. In the coarsegrained approach, sets of design signals are assigned to different processor cores and routed concurrently. Communication between cores is through the MPI (message passing interface) communications protocol. In the finegrained approach, the task of routing an individual load pin on a signal is parallelized using threads. Specifically, as FPGA routing resources are traversed during maze expansion, delay calculation, costing and priority queue insertion for these resources execute concurrently. The proposed techniques provide deterministic/repeatable results. Moreover, the coarse and finegrained approaches are not mutually exclusive and can be used in tandem. Results show that on a 4core processor, the techniques improve router runtime by ∼2.1×, on average, with no significant impact on circuit speed performance or interconnect resource usage. I.
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.
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.
Distributed Negative Cycle Detection Algorithms
"... Several new distributed algorithms for the single source shortest paths and for the negative cycle detection problems on arbitrary directed graphs given by adjacency list are developed, theoretically analysed, proved correct, and experimentally compared. The algorithms are to be performed on cluste ..."
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Several new distributed algorithms for the single source shortest paths and for the negative cycle detection problems on arbitrary directed graphs given by adjacency list are developed, theoretically analysed, proved correct, and experimentally compared. The algorithms are to be performed on clusters of workstations that communicate via a message passing mechanism.
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.