Computing L(p, 1)-Labeling with Combined Parameters

Tesshu Hanaka, Kazuma Kawai, Hirotaka Ono

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


Given a graph, an L(p, 1)-labeling of the graph is an assignment f from the vertex set to the set of nonnegative integers such that for any pair of vertices (u, v), | f(u) - f(v) | ≥ p if u and v are adjacent, and f(u) ≠ f(v) if u and v are at distance 2. The L(p, 1)-labeling problem is to minimize the span of f (i.e., maxu V(f(u) ) - minu V(f(u) ) + 1 ). It is known to be NP-hard even for graphs of maximum degree 3 or graphs with tree-width 2, whereas it is fixed-parameter tractable with respect to vertex cover number. Since the vertex cover number is a kind of the strongest parameter, there is a large gap between tractability and intractability from the viewpoint of parameterization. To fill up the gap, in this paper, we propose new fixed-parameter algorithms for L(p, 1)-Labeling by the twin cover number plus the maximum clique size and by the tree-width plus the maximum degree. These algorithms reduce the gap in terms of several combinations of parameters.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 15th International Conference and Workshops, WALCOM 2021, Proceedings
EditorsRyuhei Uehara, Seok-Hee Hong, Subhas C. Nandy
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages13
ISBN (Print)9783030682101
Publication statusPublished - 2021
Externally publishedYes
Event15th International Conference on Algorithms and Computation, WALCOM 2021 - Virtual, Online
Duration: Feb 28 2021Mar 2 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12635 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th International Conference on Algorithms and Computation, WALCOM 2021
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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