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A better approximation for minimum average routing path clustering problems in 2-D underwater sensor networks. (English) Zbl 1189.68177

Summary: Previously, we proposed the Minimum Average Routing Path Clustering Problem (MARP-CP) 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 the Minimum Weight Dominating Set Problem (MWDSP), namely MWDSP-R. In addition, we showed that the Performance Ratio (PR) of the \(\alpha\)-approximation algorithm for MWDSP-R is \(3\alpha\) for MARPCP. Based on this result, we showed the existence of a \((15 + \varepsilon)\)-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 \((3+\varepsilon)\)-approximation algorithm for MARPCP.

MSC:

68W25 Approximation algorithms
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