Abstract

The problem of constructing all simple paths in an undirected graph that pairwise connect vertices from the given set is interpreted as constructing a graph that is a union of these paths. This construction relies on the computation of biconnected components and bridges of the source graph. A new algorithm which makes this computation more transparent and controllable is proposed. Its idea is to track opening and closing of chords at the depth-first search. Due to the clarity of the proposed solution, its correctness is obvious without much justification. This is its advantage over the well-known Hopcroft–Tarjan algorithm. The proposed algorithm makes self-evident the obtaining biconnected components of a graph by successive uniting its fundamental cycles that have common edges.

中文翻译：

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运输网络中简单路径图的构建：II。图的双连通性分析

摘要

在成对连接给定集合的顶点的无向图中构造所有简单路径的问题被解释为构造作为这些路径的并集的图。这种构造依赖于源图的双向连接组件和桥的计算。提出了一种使该计算更加透明和可控的新算法。它的想法是在深度优先搜索中跟踪和弦的打开和关闭。由于所提出解决方案的清晰性，它的正确性是显而易见的，没有太多理由。这是它比著名的Hopcroft-Tarjan算法的优势。所提出的算法通过连续地组合具有共同边的基本周期，使得获得图的双向连通性变得不言而喻。