Reconfiguring k-path vertex covers

Duc A. Hoang, Akira Suzuki, Tsuyoshi Yagita

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルWALCOM
ホスト出版物のサブタイトルAlgorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings
編集者M. Sohel Rahman, Kunihiko Sadakane, Wing-Kin Sung
出版社Springer
ページ133-145
ページ数13
ISBN(印刷版)9783030398804
DOI
出版ステータスPublished - 2020
イベント14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 - Singapore, Singapore
継続期間: 2020 3 312020 4 2

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
12049 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Conference

Conference14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020
国/地域Singapore
CitySingapore
Period20/3/3120/4/2

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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