{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T18:29:31Z","timestamp":1664216971626},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2009,6]]},"abstract":"<jats:p> 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 \u03b1-approximation algorithm for MWDSP-R is 3\u03b1 for MARPCP. Based on this result, we showed the existence of a (15 + \u220a)-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 + \u220a)-approximation algorithm for MARPCP. <\/jats:p>","DOI":"10.1142\/s1793830909000142","type":"journal-article","created":{"date-parts":[[2009,7,2]],"date-time":"2009-07-02T07:53:30Z","timestamp":1246521210000},"page":"175-191","source":"Crossref","is-referenced-by-count":7,"title":["A BETTER APPROXIMATION FOR MINIMUM AVERAGE ROUTING PATH CLUSTERING PROBLEM IN 2-D UNDERWATER SENSOR NETWORKS"],"prefix":"10.1142","volume":"01","author":[{"given":"WEI","family":"WANG","sequence":"first","affiliation":[{"name":"Department of Mathematics, Xi'an Jiaotong University, 710049, P. R. China"}]},{"given":"DONGHYUN","family":"KIM","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, 2601 North Floyd Road, Richardson, TX 75083, USA"}]},{"given":"JAMES","family":"WILLSON","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, 2601 North Floyd Road, Richardson, TX 75083, USA"}]},{"given":"BHAVANI","family":"THURAISINGHAM","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, 2601 North Floyd Road, Richardson, TX 75083, USA"}]},{"given":"WEILI","family":"WU","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, 2601 North Floyd Road, Richardson, TX 75083, USA"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.adhoc.2005.01.004"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/COMST.2005.1423333"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024688116418"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.11.015"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S1389-1286(01)00302-4"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1137\/0211025"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830909000142","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T11:57:53Z","timestamp":1565179073000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830909000142"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":6,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2009,6]]}},"alternative-id":["10.1142\/S1793830909000142"],"URL":"https:\/\/doi.org\/10.1142\/s1793830909000142","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}