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An Evolutionary Formulation of the Crossing Number Problem

Author

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  • Che Sheng Gan
  • Wee Chiat Alan Tan
  • Voon Chet Koo
  • Kwang Hwai Mak

Abstract

A graph drawing algorithm is presented which results in complete graphs having minimum crossings equal to that of Guy's conjecture. It is then generalized and formulated in an evolutionary algorithm (EA) to perform constrained search for the crossing numbers. The main objective of this work is to present a suitable two-dimensional scheme which can greatly reduce the complexity of finding crossing numbers by using computer. Program performance criteria are presented and discussed. It is shown that the EA implementation provides good confirmation of the predicted crossing numbers.

Suggested Citation

  • Che Sheng Gan & Wee Chiat Alan Tan & Voon Chet Koo & Kwang Hwai Mak, 2009. "An Evolutionary Formulation of the Crossing Number Problem," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-10, September.
    • Handle: RePEc:hin:jnddns:154015
    DOI: 10.1155/2009/154015
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