Abstract.
We consider the problem of preprocessing an n -vertex 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(α(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 β ) , for any constant 0 < β < 1 . Furthermore, an algorithm of independent interest is given: computing a shortest path tree, or finding a negative cycle in linear time.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received October 30, 1996; revised May 12, 1997.
Rights and permissions
About this article
Cite this article
Chaudhuri, S., Zaroliagis, C. Shortest Paths in Digraphs of Small Treewidth. Part I: Sequential Algorithms . Algorithmica 27, 212–226 (2000). https://doi.org/10.1007/s004530010016
Issue Date:
DOI: https://doi.org/10.1007/s004530010016