TY - GEN
T1 - Reconfiguring k-path vertex covers
AU - Hoang, Duc A.
AU - Suzuki, Akira
AU - Yagita, Tsuyoshi
N1 - Funding Information:
This work is partially supported by JSPS KAKENHI Grant Numbers JP17K12636, JP18H04091, and JP19K24349, and JST CREST Grant Number JPMJCR1402.
Funding Information:
This work is partially supported by JSPSKAKENHI Grant Numbers JP17K12636, JP18H04091, and JP19K24349, and JSTCREST Grant Number JPMJCR1402.
PY - 2020
Y1 - 2020
N2 - A vertex subset I of a graph G is called a k-path vertex cover if every path on k vertices in G contains at least one vertex from I. The k -Path Vertex Cover Reconfiguration (k -PVCR) problem asks if one can transform one k-path vertex cover into another via a sequence of k-path vertex covers where each intermediate member is obtained from its predecessor by applying a given reconfiguration rule exactly once. We investigate the computational complexity of k -PVCR from the viewpoint of graph classes under the well-known reconfiguration rules: TS, TJ, and TAR. The problem for k = 2, known as the Vertex Cover Reconfiguration (VCR) problem, has been well-studied in the literature. We show that certain known hardness results for VCR on different graph classes including planar graphs, bounded bandwidth graphs, chordal graphs, and bipartite graphs, can be extended for k -PVCR. In particular, we prove a complexity dichotomy for k -PVCR on general graphs: on those whose maximum degree is 3 (and even planar), the problem is PSPACE-complete, while on those whose maximum degree is 2 (i.e., paths and cycles), the problem can be solved in polynomial time. Additionally, we also design polynomial-time algorithms for k -PVCR on trees under each of TJ and TAR. Moreover, on paths, cycles, and trees, we describe how one can construct a reconfiguration sequence between two given k-path vertex covers in a yes-instance. In particular, on paths, our constructed reconfiguration sequence is shortest.
AB - A vertex subset I of a graph G is called a k-path vertex cover if every path on k vertices in G contains at least one vertex from I. The k -Path Vertex Cover Reconfiguration (k -PVCR) problem asks if one can transform one k-path vertex cover into another via a sequence of k-path vertex covers where each intermediate member is obtained from its predecessor by applying a given reconfiguration rule exactly once. We investigate the computational complexity of k -PVCR from the viewpoint of graph classes under the well-known reconfiguration rules: TS, TJ, and TAR. The problem for k = 2, known as the Vertex Cover Reconfiguration (VCR) problem, has been well-studied in the literature. We show that certain known hardness results for VCR on different graph classes including planar graphs, bounded bandwidth graphs, chordal graphs, and bipartite graphs, can be extended for k -PVCR. In particular, we prove a complexity dichotomy for k -PVCR on general graphs: on those whose maximum degree is 3 (and even planar), the problem is PSPACE-complete, while on those whose maximum degree is 2 (i.e., paths and cycles), the problem can be solved in polynomial time. Additionally, we also design polynomial-time algorithms for k -PVCR on trees under each of TJ and TAR. Moreover, on paths, cycles, and trees, we describe how one can construct a reconfiguration sequence between two given k-path vertex covers in a yes-instance. In particular, on paths, our constructed reconfiguration sequence is shortest.
KW - Combinatorial Reconfiguration
KW - Computational complexity
KW - PSPACE-completeness
KW - Polynomial-time algorithms
KW - k-path vertex cover
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U2 - 10.1007/978-3-030-39881-1_12
DO - 10.1007/978-3-030-39881-1_12
M3 - Conference contribution
AN - SCOPUS:85080945909
SN - 9783030398804
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 133
EP - 145
BT - WALCOM
A2 - Rahman, M. Sohel
A2 - Sadakane, Kunihiko
A2 - Sung, Wing-Kin
PB - Springer
T2 - 14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020
Y2 - 31 March 2020 through 2 April 2020
ER -