An evolutionary algorithm for graph planarisation by vertex deletion

Pinheiro, Rodrigo Lankaites and Constantino, Ademir Aparecido and de Mendonca, Candido F. X. and Landa-Silva, Dario (2014) An evolutionary algorithm for graph planarisation by vertex deletion. In: 16th International Conference on Enterprise Information Systems (ICEIS 2014), 27-30 April, 2014, Lisbon, Portugal.

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Abstract

A non-planar graph can only be planarised if it is structurally modified. This work presents a new heuristic algorithm that uses vertices deletion to modify a non-planar graph in order to obtain a planar subgraph. The proposed algorithm aims to delete a minimum number of vertices to achieve its goal. The vertex deletion number of a graph G = (V,E) is the smallest integer k ? 0 such that there is an induced planar subgraph of G obtained by the removal of k vertices of G. Considering that the corresponding decision problem is NPcomplete and an approximation algorithm for graph planarisation by vertices deletion does not exist, this work proposes an evolutionary algorithm that uses a constructive heuristic algorithm to planarise a graph. This constructive heuristic has time complexity of O(n+m), where m = |V| and n = |E|, and it is based on the PQ-trees data structure and on the vertex deletion operation. The algorithm performance is verified by means of case studies.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Published in: Proceedings of the 16th International Conference on Enterprise Information Systems, ISBN 9789897580277, pages 464-471. DOI: 10.5220/0004883704640471
Keywords: evolutionary algorithms, graphical data representation
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Computer Science
Depositing User: Landa-Silva, Dario
Date Deposited: 22 Jan 2016 11:25
Last Modified: 13 Sep 2016 23:22
URI: http://eprints.nottingham.ac.uk/id/eprint/31330

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