Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 154015, 10 pages
doi:10.1155/2009/154015
Research Article

An Evolutionary Formulation of the Crossing Number Problem

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

Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Melaka, Malaysia

Received 24 September 2008; Revised 31 March 2009; Accepted 2 July 2009

Academic Editor: B. Sagar

Copyright © 2009 Che Sheng Gan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.