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.

中文翻译：

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基本变量邻域搜索用于最小座位安排问题

最小坐姿安排（MinSA）问题是一种线性布局问题，其中包括最小化将带符号的图形嵌入到一条线中时产生的错误数。先前已经通过文献中的理论和启发式方法解决了该问题。在本文中，我们提出了一种用于解决该问题的基本变量邻域搜索（BVNS）算法。首先，当只考虑正边时，我们基于输入图上的集团识别引入一种新颖的构造方案。然后将通过构造性过程获得的解用作所提出的BVNS算法的起点。描述了BVNS中本地搜索过程的几种配置的有效实现。然后将算法建议与针对不同引用实例集的MinSA的现有技术中的现有方法进行比较。非参数统计测试支持的获得结果表明，BVNS可以被视为MinSA的最新技术。