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Abstract: 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--length cycle is introduced during weight-decrease operations it is detected by the algorithms. The proposed algorithms explicitly deal with zero--length cycles. The cost of update operations... (Update)
Context of citations to this paper: More
.... 7, 8, 11, 26, 27, 28, 32] Only recently, fully dynamic algorithms have started to appear for maintenance of shortest path trees [18, 19, 30] and transitive closure [9, 23, 24, 25] However, despite the number of interesting theoretical results achieved, very little has been...
...design, it is often easy to cast the problem of design space exploration in a way that benefits from this approach. Several researchers[4, 5, 6] have worked on the area of incremental computation. They have presented analyses of algorithms for the shortest path problem and...
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3: Improved algorithms for dynamic shortest paths - Djidjev, Pantziou et al. - 1999
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BibTeX entry: (Update)
D. Frigioni, A. Marchetti-Spaccamela, U. Nanni. Fully dynamic shortest paths and negative cycles detection in digraphs with arbitrary arc weights. In Proc. 6th European Symposium on Algorithms, pp. 320-331. Lecture Notes in Computer Science, vol. 1461, 1998. http://citeseer.ist.psu.edu/frigioni98fully.html More
@inproceedings{ frigioni98fully,
author = "Daniele Frigioni and Alberto Marchetti-Spaccamela and Umberto Nanni",
title = "Fully Dynamic Shortest Paths and Negative Cycles Detection on Digraphs with Arbitrary Arc Weights",
booktitle = "European Symposium on Algorithms",
pages = "320-331",
year = "1998",
url = "citeseer.ist.psu.edu/frigioni98fully.html" }
Citations (may not include all citations):310 A note on two problems in connection with graphs (context) - Dijkstra - 1959
151 Algorithms and Applications (context) - Ahuia, Magnanti et al. - 1993
50 Incremental algorithms for minimal length paths (context) - Ausiello, Italiano et al. - 1991
49 Incremental Evaluation of Computational Circuits (context) - Alpern, Hoover et al. - 1990
49 An incremental algorithm for a generalization of the shortes.. - Ramalingam, Reps - 1996
39 Faster shortest-path algorithms for planar graphs - Klein, Rao et al. - 1994
33 Updating distances in dynamic graphs (context) - Even, Gazit - 1985
33 Bounded incremental computation (context) - Ramalingam - 1996
26 the computational complexity of dynamic graph problems - Ramalingam, Reps - 1996
26 Scaling algorithms for the shortest paths problem (context) - Goldberg - 1995
22 graphs have pagenumber O (context) - Malitz - 1994
22 Planar orientations with low out-degree and compaction of ad.. - Chrobak, Eppstein - 1991
21 Shortest path queries in digraphs of small treewidth (context) - Chaudhuri, Zaroliagis - 1995
18 A dynamization of the all-pairs least cost path problem (context) - Rohnert
14 Fully dynamic output bounded single source shortest path pro.. - Frigioni, Marchetti-Spaccamela et al. - 1996
10 Semi dynamic algorithms for maintaining single source shorte.. - Frigioni, Marchetti-Spaccamela et al.
9 Experimental analysis of dynamic algorithms for the single s.. - Frigioni, Ioffreda et al. - 1997
9 Semi dynamic shortest paths and breadth-first search on digr.. - Franciosa, Frigioni et al. - 1997
The graph only includes citing articles where the year of publication is known.
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Dynamically Switching Vertices in Planar Graphs - Frigioni, Italiano (1999) (Correct)
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