Methods for determining cycles of a specific length in undirected graphs with edge weights

R. Lewis (), P. Corcoran () and A. Gagarin ()
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R. Lewis: Cardiff University
P. Corcoran: Cardiff University
A. Gagarin: Cardiff University

Journal of Combinatorial Optimization, 2023, vol. 46, issue 5, No 2, 23 pages

Abstract: Abstract In this paper, we consider the $${{\mathcal{N}\mathcal{P}}}$$ N P -hard problem of determining fixed-length cycles in undirected edge-weighted graphs. Two solution methods are proposed, one based on integer programming (IP) and one that uses bespoke local search operators. These methods are executed under a common algorithmic framework that seeks to partition problem instances into a series of smaller sub-problems. Large-scale empirical tests indicate that the local search algorithm is generally preferable to IP, even with short run times. However, it can still produce suboptimal solutions, even with relatively small graphs.

Keywords: Graph theory; Cycles; Integer programming; Local search; Great deluge (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-023-01091-w

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