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A memetic algorithm for the cyclic antibandwidth maximization problem

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Abstract

The cyclic antibandwidth problem is to embed the vertices of a graph G of n vertices on a cycle C n such that the minimum distance (measured in the cycle) of adjacent vertices is maximized. Exact results/conjectures for this problem exist in the literature for some standard graphs, such as paths, cycles, two-dimensional meshes, and tori, but no algorithm has been proposed for the general graphs in the literature reviewed by us so far. In this paper, we propose a memetic algorithm for the cyclic antibandwidth problem (MACAB) that can be applied on arbitrary graphs. An important feature of this algorithm is the use of breadth first search generated level structures of a graph to explore a variety of solutions. A novel greedy heuristic is designed which explores these level structures to label the vertices of the graph. The algorithm achieves the exact cyclic antibandwidth of all the standard graphs with known optimal values. Based on our experiments we conjecture the cyclic antibandwidth of three-dimensional meshes, hypercubes, and double stars. Experiments show that results obtained by MACAB are substantially better than those given by genetic algorithm.

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Notes

  1. Refers to amount of time MATLAB takes to complete the operations specified.

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Acknowledgments

This work is supported by UGC vide letter no 36-66/2008 (SR). The authors would like to thank anonymous referees for their valuable comments and suggestions which have helped improve the quality and readability of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Dayalbagh Educational Institute, Agra, India

    Richa Bansal & Kamal Srivastava

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  1. Richa Bansal
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  2. Kamal Srivastava
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Correspondence to Richa Bansal.

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Bansal, R., Srivastava, K. A memetic algorithm for the cyclic antibandwidth maximization problem. Soft Comput 15, 397–412 (2011). https://doi.org/10.1007/s00500-009-0538-6

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