{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T16:53:26Z","timestamp":1770137606871,"version":"3.49.0"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,7,24]],"date-time":"2015-07-24T00:00:00Z","timestamp":1437696000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["11471003"],"award-info":[{"award-number":["11471003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Natural Science Foundation of the Jiangsu Higher Education Institutions of China","award":["13KJB1100188"],"award-info":[{"award-number":["13KJB1100188"]}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["11471016"],"award-info":[{"award-number":["11471016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["61222201"],"award-info":[{"award-number":["61222201"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100013286","name":"SRFDP","doi-asserted-by":"crossref","award":["20126501110001"],"award-info":[{"award-number":["20126501110001"]}],"id":[{"id":"10.13039\/501100013286","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Xinjiang Talent Youth Project","award":["2013711011"],"award-info":[{"award-number":["2013711011"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2017,1]]},"DOI":"10.1007\/s10878-015-9937-z","type":"journal-article","created":{"date-parts":[[2015,7,23]],"date-time":"2015-07-23T10:52:56Z","timestamp":1437648776000},"page":"106-122","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A PTAS for minimum weighted connected vertex cover $$P_3$$ P 3 problem in 3-dimensional wireless sensor networks"],"prefix":"10.1007","volume":"33","author":[{"given":"Limin","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenxue","family":"Du","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoyan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,7,24]]},"reference":[{"issue":"3","key":"9937_CR1","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.adhoc.2005.01.004","volume":"3","author":"IF Akyildiz","year":"2005","unstructured":"Akyildiz IF, Pompili D, Melodia T (2005) Underwater acoustic sensor networks: research challenges. Ad Hoc Netw 3(3):257\u2013279","journal-title":"Ad Hoc Netw"},{"key":"9937_CR2","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1016\/j.dam.2011.04.008","volume":"159","author":"B Bre\u0161ar","year":"2011","unstructured":"Bre\u0161ar B, Kardo\u0161 F, Katreni\u010d J, Semani\u0161in G (2011) Minimum $$k$$ k -path vertex cover. Discrete Appl Math 159:1189\u20131195","journal-title":"Discrete Appl Math"},{"key":"9937_CR3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0925-7721(97)00014-X","volume":"9","author":"H Breu","year":"1998","unstructured":"Breu H, Kirkpatrick DG (1998) Unit disk graph recognition is NP-hard. Comput Geom Theory Appl 9:3\u201324","journal-title":"Comput Geom Theory Appl"},{"key":"9937_CR4","volume-title":"Graph theory, graduate texts in mathematics 244","author":"JA Bondy","year":"2008","unstructured":"Bondy JA, Murty USR (2008) Graph theory, graduate texts in mathematics 244. Springer, New York"},{"key":"9937_CR5","volume-title":"Design and analysis of approximation algorithms","author":"DZ Du","year":"2012","unstructured":"Du DZ, Ko KI, Hu XD (2012) Design and analysis of approximation algorithms. Springer, New York"},{"key":"9937_CR6","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1007\/s10878-010-9315-9","volume":"22","author":"LD Fan","year":"2011","unstructured":"Fan LD, Zhang Z, Wang W (2011) PTAS for minimum weighted connected vertex cover problem with $$c$$ c -local condition in unit disk graphs. J Comb Optim 22:663\u2013673","journal-title":"J Comb Optim"},{"key":"9937_CR7","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1137\/0132071","volume":"32","author":"MR Garey","year":"1977","unstructured":"Garey MR, Johnson DS (1977) The rectilinear Steiner tree is NP-complete. SIAM J Appl Math 32:826\u2013834","journal-title":"SIAM J Appl Math"},{"key":"9937_CR8","volume-title":"Computers and intractability","author":"MR Garey","year":"1979","unstructured":"Garey MR, Johnson DS (1979) Computers and intractability. W.H. Freeman and Company, San Francisco"},{"key":"9937_CR9","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1007\/s10898-011-9831-x","volume":"56","author":"XL Liu","year":"2013","unstructured":"Liu XL, Lu HL, Wang W, Wu WL (2013) PTAS for the minimum $$k$$ k -path connected vertex cover problem in unit disk graphs. J Glob Optim 56:449\u2013458","journal-title":"J Glob Optim"},{"key":"9937_CR10","doi-asserted-by":"crossref","DOI":"10.1201\/9781439821916","volume-title":"Handbook of applied cryptography","author":"AJ Menezes","year":"1996","unstructured":"Menezes AJ, van Oorschot PC, Vanstone SA (1996) Handbook of applied cryptography. CRC Press, Boca Raton"},{"key":"9937_CR11","doi-asserted-by":"crossref","unstructured":"Novotny M (2010) Design and analysis of a generalized canvas protocol. In: Proceedings of WISTP, LNCS, vol 6033, pp 106\u2013121","DOI":"10.1007\/978-3-642-12368-9_8"},{"key":"9937_CR12","doi-asserted-by":"crossref","first-page":"7044","DOI":"10.1016\/j.tcs.2011.09.013","volume":"412","author":"JH Tu","year":"2011","unstructured":"Tu JH, Zhou WL (2011) A primal-dual approximation algorithm for the vertex cover $$P_{3}$$ P 3 problem. Theoret Comput Sci 412:7044\u20137048","journal-title":"Theoret Comput Sci"},{"key":"9937_CR13","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1016\/j.ipl.2011.04.009","volume":"111","author":"JH Tu","year":"2011","unstructured":"Tu JH, Zhou WL (2011) A factor 2 approximation algorithm for the vertex cover $$P_{3}$$ P 3 problem. Inform Process Lett 111:683\u2013686","journal-title":"Inform Process Lett"},{"key":"9937_CR14","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1109\/TC.1981.6312176","volume":"30","author":"LG Valiant","year":"1981","unstructured":"Valiant LG (1981) Universality considerations in VLSI circuits. IEEE Trans Comput 30:135\u2013140","journal-title":"IEEE Trans Comput"},{"key":"9937_CR15","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1002\/(SICI)1097-0037(199612)28:4<187::AID-NET3>3.0.CO;2-H","volume":"28","author":"LS Wang","year":"1996","unstructured":"Wang LS, Jiang T (1996) An approximation scheme for some steiner tree problems in the plane. Networks 28:187\u2013193","journal-title":"Networks"},{"key":"9937_CR16","doi-asserted-by":"crossref","unstructured":"Wang Y, Wang W, Li XY (2005) Distributed low-cost backbone formation for wireless ad hoc networks. In: Proceedings of the 6th ACM international symposium on mobile ad hoc networking and computing (MOBIHOC), 2\u201313","DOI":"10.1145\/1062689.1062692"},{"key":"9937_CR17","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.tcs.2015.01.005","volume":"571","author":"LM Wang","year":"2015","unstructured":"Wang LM, Zhang XY, Zhang Z, Broersma HJ (2015) A PTAS for the minimum weight connected vertex cover $$P_{3}$$ P 3 problem on unit disk graphs. Theoret Comput Sci 571:58\u201366","journal-title":"Theoret Comput Sci"},{"key":"9937_CR18","doi-asserted-by":"crossref","first-page":"2585","DOI":"10.1007\/978-1-4419-7997-1_60","volume-title":"Handbook of combinatorial optimization","author":"Z Zhang","year":"2013","unstructured":"Zhang Z, Wu WL (2013) Partition in high dimensional spaces. In: Pardalos PM, Du DZ, Graham RL (eds) Handbook of combinatorial optimization. Springer, New York, pp 2585\u20132624"},{"key":"9937_CR19","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/s10898-008-9384-9","volume":"45","author":"Z Zhang","year":"2009","unstructured":"Zhang Z, Gao XF, Wu WL, Du DZ (2009) A PTAS for minimum connected dominating set in $$3$$ 3 -dimensional Wireless sensor networks. J Glob Optim 45:451\u2013458","journal-title":"J Glob Optim"},{"key":"9937_CR20","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/s10878-010-9357-z","volume":"23","author":"X Zhu","year":"2010","unstructured":"Zhu X, Wang W, Shan S, Wang Z (2010) A PTAS for the minimum weighted dominating set problem with smooth weights on unit disk graphs. J Glob Optim 23:443\u2013450","journal-title":"J Glob Optim"},{"key":"9937_CR21","volume-title":"Shere packings","author":"C Zong","year":"1999","unstructured":"Zong C (1999) Shere packings. Springer, New York"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-015-9937-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10878-015-9937-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-015-9937-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-015-9937-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T15:08:46Z","timestamp":1589555326000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10878-015-9937-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,24]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["9937"],"URL":"https:\/\/doi.org\/10.1007\/s10878-015-9937-z","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"value":"1382-6905","type":"print"},{"value":"1573-2886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,24]]}}}