Abstract

CASTILLO-GARCIA, Norberto  and  HERNANDEZ-HERNANDEZ, Paula. Constructive heuristic for the vertex bisection problem. J. appl. res. technol [online]. 2020, vol.18, n.4, pp.187-196.  Epub July 31, 2021. ISSN 2448-6736.  https://doi.org/10.22201/icat.24486736e.2020.18.4.1194.

The Vertex Bisection Problem (VBP) consists in partitioning a generic graph into two equally-sized subgraphs $A$ and $B$ such that the number of vertices in $A$ with at least one adjacent vertex in $B$ is minimized. This problem is NP-hard with practical applications in the telecommunication industry. In this article we propose a new constructive algorithm for VBP based on the Greedy Randomized Adaptive Search Procedure (GRASP) methodology. We call our algorithm CVBP. We compare CVBP with a previously published GRASP-based constructive algorithm (LIT) in order to assess the performance of our algorithm in practice. The results of the experiment showed that CVBP outperformed LIT by 75.83 % in solution quality. The validation of the experimental evidence was performed by the well-known Wilcoxon Signed Rank Sum Test. The test found statistical significance for a confidence level of 99.99 %. Therefore, we consider that our constructive heuristic is a good alternative to stochastically solve the Vertex Bisection Problem.

Keywords : Vertex Bisection Problem; Constructive algorithm; Heuristic optimization.

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