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Computational Study on a PTAS for Planar Dominating Set Problem
School of Computing Science, Simon Fraser University, Burnaby BC, V5A 1S6, Canada
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Received: 2 November 2012; in revised form: 10 January 2013 / Accepted: 13 January 2013 / Published: 21 January 2013
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
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Marzban, M.; Gu, Q.-P. Computational Study on a PTAS for Planar Dominating Set Problem. Algorithms 2013, 6, 43-59.
Marzban M, Gu Q-P. Computational Study on a PTAS for Planar Dominating Set Problem. Algorithms. 2013; 6(1):43-59.
Marzban, Marjan; Gu, Qian-Ping. 2013. "Computational Study on a PTAS for Planar Dominating Set Problem." Algorithms 6, no. 1: 43-59.