The complexity of dominating set reconfiguration

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...

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Bibliographic Details
Published in:Theoretical computer science Vol. 651; pp. 37 - 49
Main Authors: Haddadan, Arash, Ito, Takehiro, Mouawad, Amer E., Nishimura, Naomi, Ono, Hirotaka, Suzuki, Akira, Tebbal, Youcef
Format: Journal Article
Language:English
Published: Elsevier B.V 25.10.2016
Subjects:
Algorithms
Combinatorial reconfiguration
Complexity
Deletion
Dominating set
Forests
Graph algorithm
Graph theory
Graphs
Intervals
Reconfiguration
Dominating set
Combinatorial reconfiguration
Graph algorithm
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary: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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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2016.08.016