TY - JOUR

T1 - The complexity of dominating set reconfiguration

AU - Haddadan, Arash

AU - Ito, Takehiro

AU - Mouawad, Amer E.

AU - Nishimura, Naomi

AU - Ono, Hirotaka

AU - Suzuki, Akira

AU - Tebbal, Youcef

PY - 2016/10/25

Y1 - 2016/10/25

N2 - Suppose that we are given two dominating sets Ds and Dt of a graph G whose cardinalities are at most a given threshold k. Then, we are asked whether there exists a sequence of dominating sets of G between Ds and Dt such that each dominating set in the sequence is of cardinality at most k and can be obtained from the previous one by either adding or deleting exactly one vertex. This decision problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, forests, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence if it exists such that the number of additions and deletions is bounded by O(n), where n is the number of vertices in the input graph.

AB - Suppose that we are given two dominating sets Ds and Dt of a graph G whose cardinalities are at most a given threshold k. Then, we are asked whether there exists a sequence of dominating sets of G between Ds and Dt such that each dominating set in the sequence is of cardinality at most k and can be obtained from the previous one by either adding or deleting exactly one vertex. This decision problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, forests, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence if it exists such that the number of additions and deletions is bounded by O(n), where n is the number of vertices in the input graph.

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U2 - 10.1016/j.tcs.2016.08.016

DO - 10.1016/j.tcs.2016.08.016

M3 - Article

AN - SCOPUS:84991404907

VL - 651

SP - 37

EP - 49

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -