TY - GEN

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 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

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, trees, 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, trees, 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 - 10.1007/978-3-319-21840-3_33

DO - 10.1007/978-3-319-21840-3_33

M3 - Conference contribution

AN - SCOPUS:84951812174

SN - 9783319218397

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 398

EP - 409

BT - Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings

A2 - Dehne, Frank

A2 - Sack, Jorg-Rudiger

A2 - Stege, Ulrike

PB - Springer Verlag

T2 - 14th International Symposium on Algorithms and Data Structures, WADS 2015

Y2 - 5 August 2015 through 7 August 2015

ER -