An O(n1.75) algorithm for L(2,1)-labeling of trees

Toru Hasunuma, Toshimasa Ishii, Hirotaka Ono, Yushi Uno

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

1 被引用数 (Scopus)

抄録

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 assignment 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. Tree is one of a few classes for which the problem is polynomially solvable, but still only an time algorithm for a tree T has been known so far, where Δ is the maximum degree of T and n∈=∈|V(T)|. In this paper, we first show that an existent necessary condition for λ(T)∈=∈Δ∈+∈1 is also sufficient for a tree T with , which leads a linear time algorithm for computing λ(T) under this condition. We then show that λ(T) can be computed in time for any tree T. Combining these, we finally obtain an time algorithm, which substantially improves upon previously known results.

本文言語英語
ホスト出版物のタイトルAlgorithm Theory - SWAT 2008 - 11th Scandinavian Workshop on Algorithm Theory, Proceedings
ページ185-197
ページ数13
DOI
出版ステータス出版済み - 2008
イベント11th Scandinavian Workshop on Algorithm Theory, SWAT 2008 - Gothenburg, スウェーデン
継続期間: 7 2 20087 4 2008

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)
5124 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他11th Scandinavian Workshop on Algorithm Theory, SWAT 2008
Countryスウェーデン
CityGothenburg
Period7/2/087/4/08

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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