4 research outputs found
Reconfiguration of Minimum Steiner Trees via Vertex Exchanges
In this paper, we study the problem of deciding if there is a transformation between two given minimum Steiner trees of an unweighted graph such that each transformation step respects a prescribed reconfiguration rule and results in another minimum Steiner tree of the graph. We consider two reconfiguration rules, both of which exchange a single vertex at a time, and generalize the known reconfiguration problem for shortest paths in an unweighted graph. This generalization implies that our problems under both reconfiguration rules are PSPACE-complete for bipartite graphs. We thus study the problems with respect to graph classes, and give some boundaries between the polynomial-time solvable and PSPACE-complete cases
Reconfiguring Directed Trees in a Digraph
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.Comment: 10 page