research-article

Fully Dynamic Algorithms for Maintaining Shortest Paths Trees

Authors:

Daniele Frigioni,

Alberto Marchetti-Spaccamela,

Umberto NanniAuthors Info & Claims

Journal of Algorithms, Volume 34, Issue 2

Pages 251 - 281

https://doi.org/10.1006/jagm.1999.1048

Published: 01 February 2000 Publication History

Abstract

We propose fully dynamic algorithms for maintaining the distances and the shortest paths from a single source in either a directed or an undirected graph with positive real edge weights, handling insertions, deletions, and weight updates of edges. The algorithms require linear space and optimal query time. The cost of the update operations depends on the class of the considered graph and on the number of the output updates, i.e., on the number of vertices that, due to an edge modification, either change the distance from the source or change the parent in the shortest paths tree. We first show that, if we deal only with updates on the weights of edges, then the update procedures require O(logn) worst case time per output update for several classes of graphs, as in the case of graphs with bounded genus, bounded arboricity, bounded degree, bounded treewidth, and bounded pagenumber. For general graphs with n vertices and m edges the algorithms require O(mlogn) worst case time per output update. We also show that, if insertions and deletions of edges are allowed, then similar amortized bounds hold.

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Index Terms

Fully Dynamic Algorithms for Maintaining Shortest Paths Trees
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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Published In

cover image Journal of Algorithms

Journal of Algorithms Volume 34, Issue 2

Feb. 2000

196 pages

ISSN:0196-6774

Editors:
Zvi Galil
Columbia Univ., New York, NY
,
David S. Johnson
AT&T Bell Lab., Florham Park, NJ
,
Donald E. Knuth
Stanford Univ., Stanford, CA

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Copyright © Academic Press.

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Academic Press, Inc.

United States

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Published: 01 February 2000

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https://dl.acm.org/doi/10.1177/02783649231171646
Al Zoobi ACoudert DNisse N(2023)Finding the k Shortest Simple Paths: Time and Space Trade-offsACM Journal of Experimental Algorithmics10.1145/362656728(1-23)Online publication date: 7-Oct-2023
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