Small k-dominating sets in planar graphs with applications

Cyril Gavoille; David Peleg; André Raspaud; Eric Sopena

doi:10.1007/3-540-45477-2_19

Small k-dominating sets in planar graphs with applications

Cyril Gavoille, David Peleg, André Raspaud, Eric Sopena

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

14 Scopus citations

Abstract

A subset of nodes S in a graph G is called k-dominating if, for every node u of the graph, the distance from u to S is at most k. We consider the parameter -γk(G) defined as the cardinality of the smallest k-dominating set of G. For planar graphs, we show that for every ε ≥ 0 and for every k ≥ (5/7 + ε)D, γk(G) = 0(1/ε). For several subclasses of planar graphs of diameter D, we show that -γk(G) is bounded by a constant for k ≥ D/2. We conjecture that the same result holds for every planar graph. This problem is motivated by the design of routing schemes with compact data structures.

Original language	English
Title of host publication	Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings
Editors	Andreas Brandstadt, Van Bang Le
Publisher	Springer Verlag
Pages	201-216
Number of pages	16
ISBN (Print)	3540427074, 9783540427070
DOIs	https://doi.org/10.1007/3-540-45477-2_19
State	Published - 2001
Externally published	Yes
Event	27th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2001 - Boltenhagen, Germany Duration: 14 Jun 2001 → 16 Jun 2001

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2204
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2001
Country/Territory	Germany
City	Boltenhagen
Period	14/06/01 → 16/06/01

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001.

Access to Document

10.1007/3-540-45477-2_19

Cite this

Gavoille, C., Peleg, D., Raspaud, A., & Sopena, E. (2001). Small k-dominating sets in planar graphs with applications. In A. Brandstadt, & V. B. Le (Eds.), Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings (pp. 201-216). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2204). Springer Verlag. https://doi.org/10.1007/3-540-45477-2_19

Gavoille, Cyril ; Peleg, David ; Raspaud, André et al. / Small k-dominating sets in planar graphs with applications. Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings. editor / Andreas Brandstadt ; Van Bang Le. Springer Verlag, 2001. pp. 201-216 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Gavoille, C, Peleg, D, Raspaud, A & Sopena, E 2001, Small k-dominating sets in planar graphs with applications. in A Brandstadt & VB Le (eds), Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2204, Springer Verlag, pp. 201-216, 27th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2001, Boltenhagen, Germany, 14/06/01. https://doi.org/10.1007/3-540-45477-2_19

Small k-dominating sets in planar graphs with applications. / Gavoille, Cyril; Peleg, David; Raspaud, André et al.
Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings. ed. / Andreas Brandstadt; Van Bang Le. Springer Verlag, 2001. p. 201-216 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2204).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Gavoille C, Peleg D, Raspaud A, Sopena E. Small k-dominating sets in planar graphs with applications. In Brandstadt A, Le VB, editors, Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings. Springer Verlag. 2001. p. 201-216. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45477-2_19

Small k-dominating sets in planar graphs with applications

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