The concept of branch decomposition was first introduced by Robertson and Seymour in their proof of the Graph Minors Theorem, and can be seen as a measure of the global connectivity of a graph. Since then, branch decomposition and branchwidth have been used for computationally solving combinatorial optimization problems modeled on graphs and matroids. General branchwidth is the extension of branchwidth to any symmetric submodular function defined over a finite set. General branchwidth encompasses graphic branchwidth, matroidal branchwidth, and rankwidth. A tangle basis is related to a tangle, a notion also introduced by Robertson and Seymour; however, a tangle basis is more constructive in nature. It was shown in [I. V. Hicks. Graphs, branchwidth, and tangles! Oh my! Networks, 45:55‐60, 2005] that a tangle basis of order k is coextensive to a tangle of order k. In this paper, we revisit the construction of tangle bases computationally for other branchwidth parameters and show that the tangle basis approach is still competitive for computing optimal branch decompositions for general branchwidth.

中文翻译：

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纠结基地：再访

罗伯逊（Robertson）和西摩（Seymour）在图次要定理的证明中首先引入了分支分解的概念，并且可以将其视为对图的整体连通性的度量。从那时起，分支分解和分支宽度已用于计算解决基于图和拟阵线建模的组合优化问题。常规分支宽度是分支宽度对在有限集上定义的任何对称子模函数的扩展。常规branchwidth包括图形branchwidth，matroidal branchwidth和rankwidth。纠缠基础与纠缠有关，Robertson和Seymour也引入了一个概念。但是，纠缠基础本质上更具建设性。它显示在[IV Hicks。图形，branchwidth和缠结！天啊！网路，45：55-60，2005]该命令的纠结基础ķ是共同延伸到顺序的纠结ķ。在本文中，我们重新计算了其他分支宽度参数的缠结基的构造，并表明缠结基方法在计算一般分支宽度的最优分支分解方面仍然具有竞争力。