In this paper, we investigate the computational complexity of subgraph reconfiguration problems in directed graphs. More specifically, we focus on the problem of determining whether, given two directed trees in a digraph, there is a (reconfiguration) sequence of directed trees such that for every pair of two consecutive trees in the sequence, one of them is obtained from the other by removing an arc and then adding another arc. We show that this problem can be solved in polynomial time, whereas the problem is PSPACE-complete when we restrict directed trees in a reconfiguration sequence to form directed paths. We also show that there is a polynomial-time algorithm for finding a shortest reconfiguration sequence between two directed spanning trees.
翻译:在本文中,我们调查了定向图表中子图重新配置问题的计算复杂性。更具体地说,我们侧重于确定,如果在一份图表中给出两棵直线树,是否有(重新配置)直线树序列,这样,每对连续两棵树的序列中,每对直线树中的一对通过去除弧从另一对树中获取,然后增加另一根弧。我们表明,这个问题可以在多元时间中解决,而当我们按照重组序列将定向树限制在形成定向路径的顺序中时,问题就是PSPACE已经完成。我们还表明,在两棵直线横贯的树之间,有一个多元时算法,可以找到最短的重组序列。