Basic variable neighborhood search for the minimum sitting arrangement problem

The minimum sitting arrangement (MinSA) problem is a linear layout problem consisting in minimizing the number of errors produced when a signed graph is embedded into a line. This problem has been previously tackled by theoretical and heuristic approaches in the literature. In this paper we present a basic variable neighborhood search (BVNS) algorithm for solving the problem. First, we introduce a novel constructive scheme based on the identification of cliques from the input graph, when only the positive edges are considered. The solutions obtained by the constructive procedure are then used as a starting point for the proposed BVNS algorithm. Efficient implementations of the several configurations of the local search procedure within the BVNS are described. The algorithmic proposal is then compared with previous approaches in the state of the art for the MinSA over different sets of referred instances. The obtained results supported by non-parametric statistical tests, indicate that BVNS can be considered as the new state-of-the-art algorithm for the MinSA.