Wang, Wei; Kim, Donghyun; Willson, James; Thuraisingham, Bhavani; Wu, Weili A better approximation for minimum average routing path clustering problems in 2-D underwater sensor networks. (English) Zbl 1189.68177 Discrete Math. Algorithms Appl. 1, No. 2, 175-191 (2009). 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. Cited in 3 Documents MSC: 68W25 Approximation algorithms Keywords:polynomial time approximation scheme; underwater sensor networks; wireless network clustering; Minimum Weight Dominating Set PDFBibTeX XMLCite \textit{W. Wang} et al., Discrete Math. Algorithms Appl. 1, No. 2, 175--191 (2009; Zbl 1189.68177) Full Text: DOI References: [1] DOI: 10.1016/j.adhoc.2005.01.004 · Zbl 05387658 · doi:10.1016/j.adhoc.2005.01.004 [2] DOI: 10.1109/COMST.2005.1423333 · doi:10.1109/COMST.2005.1423333 [3] DOI: 10.1023/A:1024688116418 · Zbl 01977783 · doi:10.1023/A:1024688116418 [4] DOI: 10.1016/j.tcs.2008.11.015 · Zbl 1162.68042 · doi:10.1016/j.tcs.2008.11.015 [5] DOI: 10.1016/S1389-1286(01)00302-4 · doi:10.1016/S1389-1286(01)00302-4 [6] DOI: 10.1137/0211025 · Zbl 0478.68043 · doi:10.1137/0211025 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.