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Authors: Rodrigo Lankaites Pinheiro 1 ; Ademir Aparecido Constantino 2 ; Candido F. X. de Mendonça 3 and Dario Landa-Silva 1

Affiliations: 1 University of Nottingham, United Kingdom ; 2 State University of Maringá, Brazil ; 3 USP-East, Brazil

Keyword(s): Graph Planarisation, Evolutionary Algorithms, Vertex Deletion.

Related Ontology Subjects/Areas/Topics: Artificial Intelligence and Decision Support Systems ; Enterprise Information Systems ; Evolutionary Programming ; Operational Research

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 NP-complete 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 is based on the PQ-trees data structure and on the vertex deletion operation. The algorithm performance is verified by means of case studies.

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Paper citation in several formats:
Lankaites Pinheiro, R.; Constantino, A.; F. X. de Mendonça, C. and Landa-Silva, D. (2014). An Evolutionary Algorithm for Graph Planarisation by Vertex Deletion. In Proceedings of the 16th International Conference on Enterprise Information Systems - Volume 3: ICEIS; ISBN 978-989-758-027-7; ISSN 2184-4992, SciTePress, pages 464-471. DOI: 10.5220/0004883704640471

@conference{iceis14,
author={Rodrigo {Lankaites Pinheiro}. and Ademir Aparecido Constantino. and Candido {F. X. de Mendon\c{C}a}. and Dario Landa{-}Silva.},
title={An Evolutionary Algorithm for Graph Planarisation by Vertex Deletion},
booktitle={Proceedings of the 16th International Conference on Enterprise Information Systems - Volume 3: ICEIS},
year={2014},
pages={464-471},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004883704640471},
isbn={978-989-758-027-7},
issn={2184-4992},
}

TY - CONF

JO - Proceedings of the 16th International Conference on Enterprise Information Systems - Volume 3: ICEIS
TI - An Evolutionary Algorithm for Graph Planarisation by Vertex Deletion
SN - 978-989-758-027-7
IS - 2184-4992
AU - Lankaites Pinheiro, R.
AU - Constantino, A.
AU - F. X. de Mendonça, C.
AU - Landa-Silva, D.
PY - 2014
SP - 464
EP - 471
DO - 10.5220/0004883704640471
PB - SciTePress

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