Abstract
Cyclic cutwidth minimization problem (CCMP) consists of embedding a graph onto a circle such that the maximum cutwidth in a region is minimized. It is an NP-complete problem and for some classes of graphs, exact results of cyclic cutwidth have been proved in literature. However, no algorithm has been reported for general graphs. In this paper, a memetic algorithm is proposed for CCMP in which we have designed six construction heuristics in order to generate a good initial population and also local search is employed to improve the solutions in each generational phase. The algorithm achieves optimal results for the classes of graphs with known exact results. Extensive experiments have also been conducted on some classes of graphs for which exact results are not known such as the complete split graph, join of hypercubes, toroidal meshes, cone graph and some instances of Harwell-Boeing graphs which are a subset of public domain Matrix Market library. Trends observed in the experimental results for some of the classes of graphs have led to conjectures for cyclic cutwidth.
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Acknowledgments
We thank the anonymous referees for their valuable comments that helped us to considerably improve the quality of this paper. The first author also acknowledges UGC, INDIA for MANF fellowship [MANF-2014- 15-JAI-UTT-38830].
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Jain, P., Srivastava, K. & Saran, G. Minimizing cyclic cutwidth of graphs using a memetic algorithm. J Heuristics 22, 815–848 (2016). https://doi.org/10.1007/s10732-016-9319-4
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DOI: https://doi.org/10.1007/s10732-016-9319-4