A Linear Time Algorithm for L(2,1)-Labeling of Trees

Toru Hasunuma, Toshimasa Ishii, Hirotaka Ono, Yushi Uno

研究成果: 著書/レポートタイプへの貢献会議での発言

16 引用 (Scopus)

抜粋

An L(2,1)-labeling of a graph G is an assignment f from the vertex set V(G) to the set of nonnegative integers such that |f(x)-f(y)|≥2 if x and y are adjacent and |f(x)-f(y)|≥1 if x and y are at distance 2, for all x and y in V(G). A k-L(2,1)-labeling is an L(2,1)-labeling f:V(G)→{0,...,k}, and the L(2,1)-labeling problem asks the minimum k, which we denote by λ(G), among all possible assignments. It is known that this problem is NP-hard even for graphs of treewidth 2, and tree is one of very few classes for which the problem is polynomially solvable. The running time of the best known algorithm for trees had been O(Δ4.5 n) for more than a decade, and an O( min {n 1.751.5 n})-time algorithm has appeared recently, where Δ is the maximum degree of T and n=|V(T)|, however, it has been open if it is solvable in linear time. In this paper, we finally settle this problem for L(2,1)-labeling of trees by establishing a linear time algorithm.

元の言語英語
ホスト出版物のタイトルAlgorithms - ESA 2009 - 17th Annual European Symposium, Proceedings
ページ35-46
ページ数12
DOI
出版物ステータス出版済み - 11 2 2009
イベント17th Annual European Symposium on Algorithms, ESA 2009 - Copenhagen, デンマーク
継続期間: 9 7 20099 9 2009

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)
5757 LNCS
ISSN(印刷物)0302-9743
ISSN(電子版)1611-3349

その他

その他17th Annual European Symposium on Algorithms, ESA 2009
デンマーク
Copenhagen
期間9/7/099/9/09

    フィンガープリント

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

これを引用

Hasunuma, T., Ishii, T., Ono, H., & Uno, Y. (2009). A Linear Time Algorithm for L(2,1)-Labeling of Trees. : Algorithms - ESA 2009 - 17th Annual European Symposium, Proceedings (pp. 35-46). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 5757 LNCS). https://doi.org/10.1007/978-3-642-04128-0_4