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Determining fixed-length paths in directed and undirected edge-weighted graphs

Hambly, Daniel, Lewis, Rhydian ORCID: and Corcoran, Padraig ORCID: 2024. Determining fixed-length paths in directed and undirected edge-weighted graphs. Presented at: Symposium on Experimental Algorithms (SEA) 2024, Vienna, Austria, 24-26 July 2024.

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In this paper, we examine the N P-hard problem of identifying fixed-length s-t paths in edge-weighted graphs – that is, a path of a desired length k from a source vertex s to a target vertex t. Many existing strategies look at paths whose lengths are determined by the number of edges in the path. We, however, look at the length of the path as the sum of the edge weights. Here, three exact algorithms for this problem are proposed: the first based on an integer programming (IP) formulation, the second a backtracking algorithm, and the third based on an extension of Yen’s algorithm. Analysis of these algorithms on random graphs shows that the backtracking algorithm performs best on smaller values of k, whilst the IP is preferable for larger values of k.

Item Type: Conference or Workshop Item (Paper)
Date Type: Completion
Status: Unpublished
Schools: Mathematics
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Date of First Compliant Deposit: 25 April 2024
Last Modified: 20 May 2024 11:08

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