Directed shortest paths via approximate cost balancing

Orlin, James B. and Végh, László A. ORCID: 0000-0003-1152-200X (2023) Directed shortest paths via approximate cost balancing. Journal of the ACM, 70 (1). ISSN 0004-5411

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Abstract

We present an O(nm) algorithm for all-pairs shortest paths computations in a directed graph with n nodes, m arcs, and nonnegative integer arc costs. This matches the complexity bound attained by Thorup [31] for the all-pairs problems in undirected graphs. The main insight is that shortest paths problems with approximately balanced directed cost functions can be solved similarly to the undirected case. The algorithm finds an approximately balanced reduced cost function in an O(m √ n log n) preprocessing step. Using these reduced costs, every shortest path query can be solved in O(m) time using an adaptation of Thorup’s component hierarchy method. The balancing result can also be applied to the ℓ∞-matrix balancing problem.

Item Type:	Article
Official URL:	https://dl.acm.org/journal/jacm
Additional Information:	© 2022 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	31 Oct 2022 10:09
Last Modified:	12 Dec 2024 03:22
URI:	http://eprints.lse.ac.uk/id/eprint/117210

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