Exact methods for the longest induced cycle problem

The longest induced (or chordless) cycle problem is a graph problem classified as NP-complete and involves the task of determining the largest possible subset of vertices within a graph in such a way that the induced subgraph forms a cycle. Within this paper, we present three integer linear programs...

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Bibliographic Details
Published inCroatian Operational Research Review Vol. 15; no. 2; pp. 199 - 212
Main Authors G.-Tóth, Boglárka, Vinkó, Tamás, Anaqreh, Ahmad Turki
Format Journal Article
LanguageEnglish
Published Zagreb Croatian Operational Research Society (CRORS) 2024
Croatian Operational Research Society
Subjects
Algorithms
Apexes
branch-and-cut algorithm
Graph theory
Graphs
Integer programming
Investigations
Linear programming
longest chordless cycle
longest induced cycle
Mixed integer
mixed integer linear programming
valid inequalities
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Summary:The longest induced (or chordless) cycle problem is a graph problem classified as NP-complete and involves the task of determining the largest possible subset of vertices within a graph in such a way that the induced subgraph forms a cycle. Within this paper, we present three integer linear programs specifically formulated to yield optimal solutions for this problem. The branch-and-cut algorithm has been used for two models that cannot be directly solved by any MILP solver. To demonstrate the computational efficiency of these methods, we utilize them on a range of real-world graphs as well as random graphs. Additionally, we conduct a comparative analysis against approaches previously proposed in the literature.
ISSN:1848-9931
1848-0225
1848-9931
DOI:10.17535/crorr.2024.0016