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

N1 - Funding Information:
We thank anonymous referees of the preliminary version [12] and of this journal version for their helpful suggestions. This work is partially supported by the Natural Sciences and Engineering Research Council of Canada (A. Mouawad, N. Nishimura, and Y. Tebbal) and by MEXT/JSPS KAKENHI JP15H00849 and JP16K00004 (T. Ito), JP25104521 and JP26540005 (H. Ono), and JP26730001 (A. Suzuki).
Publisher Copyright:
© 2016 Elsevier B.V.

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.

KW - Combinatorial reconfiguration

KW - Dominating set

KW - Graph algorithm

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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 -