2000 character limit reached
Exact Methods for the Longest Induced Cycle Problem (2311.15899v1)
Published 27 Nov 2023 in cs.DM
Abstract: 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. 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.
- INFORMS Journal on Computing. 34(4),1970–1986 (2022)
- Computers & Operations Research. 139, 105627 (2022)
- International Symposium on Combinatorial Optimization, 89–101 (2020)
- Gurobi Optimization Inc. Gurobi Optimizer Reference Manual (2020)
- European Journal of Operational Research 278(2),546–562 (2019)
- Harvard Dataverse, (2018)
- Proceedings of the International Conference on Wireless Networks (ICWN), pp. 202–208 (2014)
- Algorithmica 65(1), 129–145 (2013)
- Walsh, Toby: Symmetry breaking constraints: Recent results. Proceedings of the AAAI Conference on Artificial Intelligence 26(1), 2192–2198 (2012)
- Lokshtanov, Daniel: Finding the longest isometric cycle in a graph. Discrete Applied Mathematics.157(12),2670–2674 (2009)
- Twenty-Second Annual IEEE Conference on Computational Complexity (CCC’07), pp. 250–263 (2007)
- Fuchs, Elena D: Longest induced cycles in circulant graphs. The Electronic Journal of Combinatorics, Article Number R52 (2005)
- West, Douglas Brent and others: Introduction to Graph Theory. Prentice Hall (2001)
- PhD thesis, TU Berlin, Berlin. (1998)
- Journal of the Operational Research Society. 43(5), 443–457 (1992)
- W. H. Freeman & Co. (1990)
- Wojciechowski, Jerzy Marian: Long induced cycles in the hypercube and colourings of graphs. University of Cambridge (1990)
- Alon, Noga: The longest cycle of a graph with a large minimal degree. Journal of Graph Theory. 10(1), 123–127 (1986)
- Journal of Information Processing. 3(2), 73–76 (1980)
- PassMark Software - CPU Benchmarks: https://www.cpubenchmark.net/compare (2023)