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Design and Implementation of a Practical I/Oefficient Shortest Paths Algorithm
"... We report on initial experimental results for a practical I/Oefficient SingleSource ShortestPaths (SSSP) algorithm on general undirected sparse graphs where the ratio between the largest and the smallest edge weight is reasonably bounded (for example integer weights in {1,...,2 32}) and the reali ..."
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We report on initial experimental results for a practical I/Oefficient SingleSource ShortestPaths (SSSP) algorithm on general undirected sparse graphs where the ratio between the largest and the smallest edge weight is reasonably bounded (for example integer weights in {1,...,2 32
Bounded Incremental SingleSource ShortestPaths
"... Abstract. We consider the problem of maintaining the distances of all vertices of a directed graph from a specific vertex, its source. We show algorithms in the bounded incremental computation (BIC) model which handle the insertion or deletion of an arc (or a batch of arcs outgoing from a shared ver ..."
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vertex) in O(�δ � + δlog δ) amortized time on Cyclic>0 graphs (i.e., graphs whose cycles have strictly positive lengths), where δ  and �δ � are measures of the change in the input and output. On Cyclic≥0 graphs, maintaining shortest paths is unbounded under reasonable variants of the BIC model
Incremental ShortestPath Problem
"... The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also subsume ..."
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The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also
Directed SingleSource ShortestPaths in Linear AverageCase Time
, 2001
"... The quest for a lineartime singlesource shortestpath (SSSP) algorithm on directed graphs with positive edge weights is an ongoing hot research topic. While Thorup recently found an O(n + m) time RAM algorithm for undirected graphs with n nodes, m edges and integer edge weights in f0; : : : ; 2 ..."
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The quest for a lineartime singlesource shortestpath (SSSP) algorithm on directed graphs with positive edge weights is an ongoing hot research topic. While Thorup recently found an O(n + m) time RAM algorithm for undirected graphs with n nodes, m edges and integer edge weights in f0
AverageCase Complexity of ShortestPaths Problems
, 2001
"... We study both upper and lower bounds on the averagecase complexity of shortestpaths algorithms. It is proved that the allpairs shortestpaths problem on nvertex networks can be solved in time O(n² log n) with high probability with respect to various probability distributions on the set of inputs. ..."
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the singlesource shortestpaths problem on such networks in time O(n²) with high probability. All algorithms mentioned exploit that with high probability, the singlesource shortestpaths problem can be solved correctly by considering only a rather sparse subset of the arc set. We prove a lower bound
Experimental studies of symbolic shortestpath algorithms
 In Proceedings of the 3rd International Workshop on Experimental and Efficient Algorithms (WEA04
, 2004
"... Abstract. Graphs can be represented symbolically by the Ordered Binary Decision Diagram (OBDD) of their characteristic function. To solve problems in such implicitly given graphs, specialized symbolic algorithms are needed which are restricted to the use of functional operations offered by the OBDD ..."
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Cited by 5 (4 self)
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data structure. In this paper, two symbolic algorithms for the singlesource shortestpath problem with nonnegative positive integral edge weights are presented which represent symbolic versions of Dijkstra’s algorithm and the BellmanFord algorithm. They execute O ( N ·log(NB) ) resp. O ( NM
Faster ShortestPath Algorithms for Planar Graphs
 STOC 94
, 1994
"... We give a lineartime algorithm for singlesource shortest paths in planar graphs with nonnegative edgelengths. Our algorithm also yields a lineartime algorithm for maximum flow in a planar graph with the source and sink on the same face. The previous best algorithms for these problems required\O ..."
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Cited by 200 (15 self)
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We give a lineartime algorithm for singlesource shortest paths in planar graphs with nonnegative edgelengths. Our algorithm also yields a lineartime algorithm for maximum flow in a planar graph with the source and sink on the same face. The previous best algorithms for these problems required
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
Results 1  10
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896,752