Maximum Domination problem

Eiji Miyano, Hirotaka Ono

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

6 Citations (Scopus)

Abstract

We consider new variants of the vertex/edge domination problems on graphs. A vertex is said to dominate itself and its all adjacent vertices, and similarly an edge is said to dominate itself and its all adjacent edges. Given an input graph G = (V;E) and an integer k, the κ-Vertex (κ-Edge) Maximum Domination (κ-MaxVD and κ-MaxED, respectively) is to find a subset D V ⊆ V of vertices (resp., D E ⊆ E of edges) with size at most k that maximizes the cardinality of dominated vertices (resp., edges). In this paper, we first show that a simple greedy strategy achieves an approximation ratio of (1 - 1=e) for both k-MaxVD and κ-MaxED. Then, we show that this approximation ratio is the best possible for κ-MaxVD unless P = NP. We also prove that, for any constant ε > 0, there is no polynomial time 1303=1304+ε approximation algorithm for κ-MaxED unless P = NP. However, if k is not larger than the size of the minimum maximal matching, κ-MaxED is 3/4-approximable in polynomial time.

Original languageEnglish
Title of host publicationTheory of Computing 2011 - Proceedings of the 17th Computing
Subtitle of host publicationThe Australasian Theory Symposium, CATS 2011
Pages55-61
Number of pages7
Publication statusPublished - Dec 1 2011
EventTheory of Computing 2011 - 17th Computing: The Australasian Theory Symposium, CATS 2011 - Perth, WA, Australia
Duration: Jan 17 2011Jan 20 2011

Publication series

NameConferences in Research and Practice in Information Technology Series
Volume119
ISSN (Print)1445-1336

Other

OtherTheory of Computing 2011 - 17th Computing: The Australasian Theory Symposium, CATS 2011
CountryAustralia
CityPerth, WA
Period1/17/111/20/11

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Computer Science Applications
  • Hardware and Architecture
  • Information Systems
  • Software

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  • Cite this

    Miyano, E., & Ono, H. (2011). Maximum Domination problem. In Theory of Computing 2011 - Proceedings of the 17th Computing: The Australasian Theory Symposium, CATS 2011 (pp. 55-61). (Conferences in Research and Practice in Information Technology Series; Vol. 119).