Results 1  10
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14
Shortest Paths in Digraphs of Small Treewidth. Part I: Sequential Algorithms
, 1995
"... We consider the problem of preprocessing an nvertex digraph with real edge weights so that subsequent queries for the shortest path or distance between any two vertices can be efficiently answered. We give algorithms that depend on the treewidth of the input graph. When the treewidth is a consta ..."
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Cited by 35 (4 self)
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We consider the problem of preprocessing an nvertex digraph with real edge weights so that subsequent queries for the shortest path or distance between any two vertices can be efficiently answered. We give algorithms that depend on the treewidth of the input graph. When the treewidth is a constant, our algorithms can answer distance queries in O(ff(n)) time after O(n) preprocessing. This improves upon previously known results for the same problem. We also give a dynamic algorithm which, after a change in an edge weight, updates the data structure in time O(n fi ), for any constant 0 ! fi ! 1. Furthermore, an algorithm of independent interest is given: computing a shortest path tree, or finding a negative cycle in linear time.
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 (12 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.
Experimental Analysis of Dynamic Algorithms for the Single Source Shortest Path Problem
 ACM Jounal of Experimental Algorithmics
, 1997
"... In this paper we propose the first experimental study of the fully dynamic single source shortest paths problem on directed graphs with positive real edge weights. In particular, we perform an experimental analysis of three different algorithms: Dijkstra's algorithm, and the two output bounded al ..."
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Cited by 19 (2 self)
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In this paper we propose the first experimental study of the fully dynamic single source shortest paths problem on directed graphs with positive real edge weights. In particular, we perform an experimental analysis of three different algorithms: Dijkstra's algorithm, and the two output bounded algorithms proposed by Ramalingam and Reps in [31] and by Frigioni, MarchettiSpaccamela and Nanni in [18], respectively. The main goal of this paper is to provide a first experimental evidence for: (a) the effectiveness of dynamic algorithms for shortest paths with respect to a traditional static approach to this problem; (b) the validity of the theoretical model of output boundedness to analyze dynamic graph algorithms. Beside random generated graphs, useful to capture the "asymptotic" behavior of algorithms, we also develope experiments by considering a widely used graph from the real world, i.e., the Internet graph. Work partially supported by the ESPRIT Long Term Research Project...
Fully Dynamic Shortest Paths and Negative Cycle Detection on Digraphs with Arbitrary Arc Weights
 In European Symposium on Algorithms
, 1998
"... We study the problem of maintaining the distances and the shortest paths from a source node in a directed graph with arbitrary arc weights, when weight updates of arcs are performed. We propose algorithms that work for any digraph and have optimal space requirements and query time. If a negative ..."
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Cited by 18 (2 self)
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We study the problem of maintaining the distances and the shortest paths from a source node in a directed graph with arbitrary arc weights, when weight updates of arcs are performed. We propose algorithms that work for any digraph and have optimal space requirements and query time. If a negativelength cycle is introduced during weightdecrease operations it is detected by the algorithms. The proposed algorithms explicitly deal with zerolength cycles. The cost of update operations depends on the class of the considered digraph and on the number of the output updates. We show that, if the digraph has a kbounded accounting function (as in the case of digraphs with genus, arboricity, degree, treewidth or pagenumber bounded by k) the update procedures require O(k \Delta n \Delta log n) worst case time. In the case of digraphs with n nodes and m arcs k = O( p m), and hence we obtain O( p m \Delta n \Delta log n) worst case time per operation, which is better for a factor o...
Improved Algorithms for Dynamic Shortest Paths
 Algorithmica
, 1996
"... We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can ..."
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Cited by 15 (3 self)
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We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. In the case of outerplanar digraphs, our data structures can be updated after any such change in only logarithmic time and a distance query is answered also in logarithmic time. In the case of planar digraphs, we give an interesting tradeoff between preprocessing, query and update times depending on the value of a certain topological parameter of the graph. Our results can be extended to nvertex digraphs of genus O(n 1\Gamma" ) for any " ? 0. Keywords: Shortest path, dynamic algorithm, planar digraph, outerplanar digraph. This work was partially supported by the NSF grant No. CCR9409191 and by the EU ESPRIT LTR Project No. 20244 (ALCOMIT). 1 Introduction 1.1 The prob...
SemiDynamic Shortest Paths and BreadthFirst Search in Digraphs
, 1996
"... In this paper we study the problem of maintaining a single source shortest path tree or a breadthfirst search tree for a directed graph, in either an incremental or decremental setting. We maintain a single source shortest path tree of a directed graph G with unit edge weights during a sequence of ..."
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Cited by 13 (4 self)
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In this paper we study the problem of maintaining a single source shortest path tree or a breadthfirst search tree for a directed graph, in either an incremental or decremental setting. We maintain a single source shortest path tree of a directed graph G with unit edge weights during a sequence of edge deletions in total time O(mn), thus obtaining a O(n) amortized time for each deletion if the sequence has length\Omega\Gamma m), where n is the number of vertices of G and m is the initial number of edges of G. To the best of our knowledge, this is the first known decremental algorithm for directed graphs with unit edge weights that is asymptotically faster than recomputing the single source shortest path tree from scratch after each deletion, which can be accomplished in O(m 2 ) total time. This result is extended to handle the case of integer edge weights in [1; C], allowing to maintain a single source shortest path tree during a sequence of edge deletions in total time O(Cmn). We...
Shortest Path Algorithms for Nearly Acyclic Directed Graphs
 Comput. Sci
, 1997
"... Abuaiadh and Kingston gave an efficient algorithm for the single source shortest path problem for a nearly acyclic graph with O(m+n log t) computing time, where m and n are the numbers of edges and vertices of the given directed graph and t is the number of deletemin operations in the priority queu ..."
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Cited by 6 (5 self)
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Abuaiadh and Kingston gave an efficient algorithm for the single source shortest path problem for a nearly acyclic graph with O(m+n log t) computing time, where m and n are the numbers of edges and vertices of the given directed graph and t is the number of deletemin operations in the priority queue manipulation. They use the Fibonacci heap for the priority queue. If the graph is acyclic, we have t = 0 and the time complexity becomes O(m + n) which is linear and optimal. They claim that if the graph...
AllPairs MinCut in Sparse Networks
, 1996
"... Algorithms are presented for the allpairs mincut problem in bounded treewidth, planar and sparse networks. The approach used is to preprocess the input nvertex network so that, afterwards, the value of a mincut between any two vertices can be efficiently computed. A tradeoff is shown between th ..."
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Cited by 5 (1 self)
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Algorithms are presented for the allpairs mincut problem in bounded treewidth, planar and sparse networks. The approach used is to preprocess the input nvertex network so that, afterwards, the value of a mincut between any two vertices can be efficiently computed. A tradeoff is shown between the preprocessing time and the time taken to compute mincuts subsequently. In particular, after an O(n log n) preprocessing of a bounded treewidth network, it is possible to find the value of a mincut between any two vertices in constant time. This implies that for such networks the allpairs mincut problem can be solved in time O(n 2 ). This algorithm is used in conjunction with a graph decomposition technique of Frederickson to obtain algorithms for sparse and planar networks. The running times depend upon a topological property, fl, of the input network. The parameter fl varies between 1 and \Theta(n); the algorithms perform well when fl = o(n). The value of a mincut can be found in t...
Distributed shortest path for directed graphs with negative edge lengths
, 2001
"... w\Delta\Theta\Xi\Pi\Sigma\Upsilon\Phi\Omega fffiflffiij`'ae/!"#$%&'()+,./012345!yA ..."
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Cited by 4 (3 self)
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w\Delta\Theta\Xi\Pi\Sigma\Upsilon\Phi\Omega fffiflffiij`'ae/!"#$%&'()+,./012345!yA
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 (1 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.