{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:37:23Z","timestamp":1767339443113,"version":"3.37.3"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T00:00:00Z","timestamp":1586304000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T00:00:00Z","timestamp":1586304000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61662088"],"award-info":[{"award-number":["61662088"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s10878-020-00568-2","type":"journal-article","created":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T16:02:30Z","timestamp":1586361750000},"page":"1964-1976","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Combinatorial approximation algorithms for the submodular multicut problem in trees with submodular penalties"],"prefix":"10.1007","volume":"44","author":[{"given":"Xiaofei","family":"Liu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3094-4347","authenticated-orcid":false,"given":"Weidong","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,4,8]]},"reference":[{"issue":"4","key":"568_CR1","doi-asserted-by":"publisher","first-page":"864","DOI":"10.1137\/S0097539792225297","volume":"23","author":"E Dahlhaus","year":"1994","unstructured":"Dahlhaus E, Johnson DS, Papadimitriou CH, Seymour PD, Yannakakis M (1994) The complexity of multiterminal cuts. SIAM J Comput 23(4):864\u2013894","journal-title":"SIAM J Comput"},{"key":"568_CR2","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/s00453-011-9526-1","volume":"63","author":"D Du","year":"2012","unstructured":"Du D, Lu R, Xu D (2012) A primal-dual approximation algorithm for the facility location problem with submodular penalties. Algorithmica 63:191\u2013200","journal-title":"Algorithmica"},{"key":"568_CR3","volume-title":"Submodular functions and optimization","author":"S Fujishige","year":"2005","unstructured":"Fujishige S (2005) Submodular functions and optimization, 2nd edn. Elsevier, Amsterdam","edition":"2"},{"issue":"1","key":"568_CR4","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/BF02523685","volume":"18","author":"N Garg","year":"1997","unstructured":"Garg N, Vazirani VV, Yannakakis M (1997) Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica 18(1):3\u201320","journal-title":"Algorithmica"},{"issue":"2","key":"568_CR5","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1137\/S0097539793243016","volume":"25","author":"N Garg","year":"2006","unstructured":"Garg N, Vazirani VV, Yannakakis M (2006) Approximate max-flow min-(multi) cut theorems and their applications. SIAM J Comput 25(2):235\u2013251","journal-title":"SIAM J Comput"},{"key":"568_CR6","unstructured":"Hayrapetyan A, Swamy C, Tardos E (2005) Network design for information networks. In: Proceedings of the sixteenth annual ACM-SIAM symposium on discrete algorithms, pp 933\u2013942"},{"key":"568_CR7","volume-title":"Integer programming and network flows","author":"TC Hu","year":"1969","unstructured":"Hu TC (1969) Integer programming and network flows. Addison-Wesley, Reading, MA"},{"key":"568_CR8","doi-asserted-by":"crossref","unstructured":"Iwata S, Nagano K (2009) Submodular function minimization under covering constraints. In: The 50th annual symposium on foundations of computer science, FOCS, pp. 671\u2013680","DOI":"10.1109\/FOCS.2009.31"},{"issue":"4","key":"568_CR9","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1145\/502090.502096","volume":"48","author":"S Iwata","year":"2001","unstructured":"Iwata S, Fleischer L, Fujishige S (2001) A combinatorial strongly polynomial algorithm for minimizing submodular functions. J ACM 48(4):761\u2013777","journal-title":"J ACM"},{"key":"568_CR10","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.tcs.2016.10.017","volume":"659","author":"N Kamiyama","year":"2017","unstructured":"Kamiyama N (2017) A note on the submodular vertex cover problem with submodular penalties. Theor Comput Sci 659:95\u201397","journal-title":"Theor Comput Sci"},{"key":"568_CR11","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1016\/j.tcs.2015.06.010","volume":"607","author":"I Kanj","year":"2015","unstructured":"Kanj I, Lin G, Liu T, Tong W, Xia G, Xu J, Yang B, Zhang F, Zhang P, Zhu B (2015) Improved parameterized and exact algorithms for cut problems on trees. Theor Comput Sci 607:455\u2013470","journal-title":"Theor Comput Sci"},{"issue":"3","key":"568_CR12","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/j.jcss.2007.06.019","volume":"74","author":"S Khot","year":"2008","unstructured":"Khot S, Regev O (2008) Vertex cover might be hard to approximateto with $$2-\\epsilon $$. J Comput Syst Sci 74(3):335\u2013349","journal-title":"J Comput Syst Sci"},{"issue":"1\u20133","key":"568_CR13","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1016\/j.tcs.2006.09.018","volume":"369","author":"A Levin","year":"2006","unstructured":"Levin A, Segev D (2006) Partial multicuts in trees. Theor Comput Sci 369(1\u20133):384\u2013395","journal-title":"Theor Comput Sci"},{"issue":"2","key":"568_CR14","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1007\/s00453-014-9911-7","volume":"73","author":"Y Li","year":"2015","unstructured":"Li Y, Du D, Xiu N, Xu D (2015) Improved approximation algorithms for the facility location problems with linear\/submodular penalties. Algorithmica 73(2):460\u2013482","journal-title":"Algorithmica"},{"issue":"1","key":"568_CR15","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/s10878-012-9565-9","volume":"27","author":"H Liu","year":"2014","unstructured":"Liu H, Zhang P (2014) On the generalized multiway cut in trees problem. J Comb Optim 27(1):65\u201377","journal-title":"J Comb Optim"},{"key":"568_CR16","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.tcs.2016.04.005","volume":"630","author":"D Xu","year":"2016","unstructured":"Xu D, Wang F, Du D, Wu C (2016) Approximation algorithms for submodular vertex cover problems with linear\/submodular penalties using primal-dual technique. Theor Comput Sci 630:117\u2013125","journal-title":"Theor Comput Sci"},{"issue":"7\u20138","key":"568_CR17","doi-asserted-by":"publisher","first-page":"1240","DOI":"10.1016\/j.dam.2012.01.016","volume":"160","author":"P Zhang","year":"2012","unstructured":"Zhang P, Zhu D, Luan J (2012) An approximation algorithm for the generalized k-multicut problem. Discrete Appl Math 160(7\u20138):1240\u20131247","journal-title":"Discrete Appl Math"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-020-00568-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-020-00568-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-020-00568-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T08:47:20Z","timestamp":1664354840000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-020-00568-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,8]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["568"],"URL":"https:\/\/doi.org\/10.1007\/s10878-020-00568-2","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"type":"print","value":"1382-6905"},{"type":"electronic","value":"1573-2886"}],"subject":[],"published":{"date-parts":[[2020,4,8]]},"assertion":[{"value":"8 April 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}