On Matchings and b-Edge Dominating Sets: A 2-Approximation Algorithm for the 3-Edge Dominating Set Problem

Social networks are increasingly becoming an outlet that is more and more powerful in spreading news and influence individuals. Compared with other traditional media outlets such as newspaper, radio, and television, social networks empower users to spread their ideological message and/or to deliver target advertising very efficiently in terms of both cost and time. In this article, the authors focus on efficiently finding dominating sets in social networks for the classical dominating set problem as well as for two related problems: partial dominating sets and d-hop dominating sets. They will present algorithms for determining efficiently a good approximation for the social network minimum dominating sets for each of the three variants. The authors ran an extensive suite of experiments to test the presented algorithms on several datasets that include real networks made available by the Stanford Network Analysis Project and synthetic networks that follow the power-law and random models that they generated for this work. The performed experiments show that the selection of the algorithm that performs best to determine efficiently the dominating set is dependent of network characteristics and the order of importance between the size of the dominating set and the time required to determine such a set.

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Approximation Algorithms for the b-Edge Dominating Set Problem and Its Related Problems

Lecture Notes in Computer Science - Computing and Combinatorics ◽

10.1007/11533719_76 ◽

2005 ◽

pp. 747-756

Author(s):

Takuro Fukunaga ◽

Hiroshi Nagamochi

Keyword(s):

Approximation Algorithms ◽

Dominating Set ◽

Edge Dominating Set ◽

Dominating Set Problem

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A BETTER APPROXIMATION FOR MINIMUM AVERAGE ROUTING PATH CLUSTERING PROBLEM IN 2-D UNDERWATER SENSOR NETWORKS

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830909000142 ◽

2009 ◽

Vol 01 (02) ◽

pp. 175-191 ◽

Cited By ~ 6

Author(s):

WEI WANG ◽

DONGHYUN KIM ◽

JAMES WILLSON ◽

BHAVANI THURAISINGHAM ◽

WEILI WU

Keyword(s):

Sensor Networks ◽

Approximation Algorithm ◽

Dominating Set ◽

Minimum Weight ◽

Performance Ratio ◽

Underwater Sensor Networks ◽

Clustering Problem ◽

Np Completeness ◽

Dominating Set Problem ◽

Special Case

Previously, we proposed Minimum Average Routing Path Clustering Problem (MARPCP) in multi-hop USNs. The goal of this problem is to find a clustering of a USN so that the average clustering-based routing path from a node to it nearest underwater sink is minimized. We relaxed MARPCP to a special case of Minimum Weight Dominating Set Problem (MWDSP), namely MWDSP-R. In addition, we showed the Performance Ratio (PR) of α-approximation algorithm for MWDSP-R is 3α for MARPCP. Based on this result, we showed the existence of a (15 + ∊)-approximation algorithm for MARPCP. In this paper, we first establish the NP-completeness of both MARPCP and MWDSP-R. Then, we propose a PTAS for MWDSP-R. By combining this result with our previous one, we have a (3 + ∊)-approximation algorithm for MARPCP.

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