Algorithms 2013, 6(1), 43-59; doi:10.3390/a6010043
Article

Computational Study on a PTAS for Planar Dominating Set Problem

email and * email
Received: 2 November 2012; in revised form: 10 January 2013 / Accepted: 13 January 2013 / Published: 21 January 2013
(This article belongs to the Special Issue Graph Algorithms)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: The dominating set problem is a core NP-hard problem in combinatorial optimization and graph theory, and has many important applications. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time approximation scheme (PTAS) for a class of NP-hard problems in planar graphs. It is mentioned that the framework can be applied to obtain an O(2ckn) time, c is a constant, (1+1/k)-approximation algorithm for the planar dominating set problem. We show that the approximation ratio achieved by the mentioned application of the framework is not bounded by any constant for the planar dominating set problem. We modify the application of the framework to give a PTAS for the planar dominating set problem. With k-outer planar graph decompositions, the modified PTAS has an approximation ratio (1 + 2/k). Using 2k-outer planar graph decompositions, the modified PTAS achieves the approximation ratio (1+1/k) in O(22ckn) time. We report a computational study on the modified PTAS. Our results show that the modified PTAS is practical.
Keywords: dominating set problem; PTAS; branch-decomposition based algorithms; planar graphs; computational study
PDF Full-text Download PDF Full-Text [150 KB, Updated Version, uploaded 22 January 2013 15:30 CET]
The original version is still available [150 KB, uploaded 21 January 2013 11:45 CET]

Export to BibTeX |
EndNote


MDPI and ACS Style

Marzban, M.; Gu, Q.-P. Computational Study on a PTAS for Planar Dominating Set Problem. Algorithms 2013, 6, 43-59.

AMA Style

Marzban M, Gu Q-P. Computational Study on a PTAS for Planar Dominating Set Problem. Algorithms. 2013; 6(1):43-59.

Chicago/Turabian Style

Marzban, Marjan; Gu, Qian-Ping. 2013. "Computational Study on a PTAS for Planar Dominating Set Problem." Algorithms 6, no. 1: 43-59.

Algorithms EISSN 1999-4893 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert