Work

k-shortest simple paths in bounded treewidth graphs

Year: 2025

Type: article

Abstract: The k -shortest simple paths problem asks to compute a set of top- k shortest simple paths from a source to a sink in a graph G = ( V , E ) with | V | = n vertices and | E | = m edges. The most well-known algorithm for solving this problem is due to Yen (1971) with time complexity in O ( k n ( m + n log ⁡ n ) ) and the fastest algorithm is due to Gotthilf and Lewenstein (2009) with time complexity in O ( k n ( m + n log ⁡ log ⁡ n ) ) . For bounded treewidth graphs, Eppstein and Kurz (2017) lowered the computational complexity to O ( k n ) by retrieving paths from the k smallest solutions of a monadic second-order formula, and to O ( n + k log ⁡ ( n ) ) to retrieve the k shortest simple distances only. In this paper, we provide an algorithm that answers k -shortest simple distances in O ( k + n ) time on graphs with treewidth at most 2, and a constructive algorithm, simpler than that of Eppstein and Kurz, that solves the k -shortest simple paths problem in O ( k n ) time on bounded treewidth graphs.

Source: Theoretical Computer Science

DOI: 10.1016/j.tcs.2025.115182

Authors: David Coudert, Andrea D'Ascenzo, Clément Rambaud

Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Université Côte d'Azur, Laboratoire d'Informatique, Signaux et Systèmes de Sophia Antipolis, Libera Università Internazionale degli Studi Sociali Guido Carli

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,880