{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T17:02:20Z","timestamp":1784739740718,"version":"3.55.0"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T00:00:00Z","timestamp":1779062400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T00:00:00Z","timestamp":1779062400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12571337"],"award-info":[{"award-number":["12571337"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371317"],"award-info":[{"award-number":["12371317"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007219","name":"Natural Science Foundation of Shanghai Municipality","doi-asserted-by":"publisher","award":["24ZR1416900"],"award-info":[{"award-number":["24ZR1416900"]}],"id":[{"id":"10.13039\/100007219","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":[[2026,7]]},"DOI":"10.1007\/s10878-026-01422-7","type":"journal-article","created":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T06:31:35Z","timestamp":1779085895000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Approximation algorithms for the minimum weight cycle\/path partition problem"],"prefix":"10.1007","volume":"51","author":[{"given":"Yaqi","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6127-1264","authenticated-orcid":false,"given":"Wei","family":"Yu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhaohui","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,18]]},"reference":[{"key":"1422_CR1","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/j.dam.2017.11.031","volume":"239","author":"A Bar-Noy","year":"2018","unstructured":"Bar-Noy A, Peleg D, Rabanca G, Vigan I (2018) Improved approximation algorithms for weighted 2-path partitions. Discret Appl Math 239:15\u201337","journal-title":"Discret Appl Math"},{"key":"1422_CR2","doi-asserted-by":"crossref","unstructured":"Berman P, Karpinski M (2005) 8\/7-approximation algorithm for (1,2)-TSP. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 641\u2013648","DOI":"10.1145\/1109557.1109627"},{"key":"1422_CR3","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1007\/s10878-020-00660-7","volume":"41","author":"Y Chen","year":"2021","unstructured":"Chen Y, Chen ZZ, Lin GH, Wang LS, Zhang A (2021) A randomized approximation algorithm for metric triangle packing. J Comb Optim 41:12\u201327","journal-title":"J Comb Optim"},{"key":"1422_CR4","volume-title":"Computers and Intractability: A Guide to the Theory of NP-completeness","author":"MR Garey","year":"1979","unstructured":"Garey MR, Johnson DS (1979) Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco"},{"issue":"2","key":"1422_CR5","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1137\/S0097539793242618","volume":"24","author":"MX Goemans","year":"1995","unstructured":"Goemans MX, Williamson DP (1995) A general approximation technique for constrained forest problems. SIAM J Comput 24(2):296\u2013317","journal-title":"SIAM J Comput"},{"issue":"2","key":"1422_CR6","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/S0020-0190(97)00097-5","volume":"63","author":"R Hassin","year":"1997","unstructured":"Hassin R, Rubinstein S (1997) An approximation algorithm for maximum packing of 3-edge paths. Inf Process Lett 63(2):63\u201367","journal-title":"Inf Process Lett"},{"issue":"4","key":"1422_CR7","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/j.disopt.2013.09.001","volume":"10","author":"R Hassin","year":"2013","unstructured":"Hassin R, Schneider O (2013) A local search algorithm for binary maximum 2-path partitioning. Discret Optim 10(4):333\u2013360","journal-title":"Discret Optim"},{"issue":"4","key":"1422_CR8","doi-asserted-by":"publisher","first-page":"2340003","DOI":"10.1142\/S0217595923400031","volume":"40","author":"S Li","year":"2023","unstructured":"Li S, Yu W (2023) Approximation algorithms for the maximum-weight cycle\/path packing problems. Asia-Pacific J Oper Res 40(4):2340003","journal-title":"Asia-Pacific J Oper Res"},{"issue":"2","key":"1422_CR9","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/j.jda.2007.01.006","volume":"6","author":"J Monnot","year":"2008","unstructured":"Monnot J, Toulouse S (2008) Approximation results for the weighted P4 partition problem. Journal of Discrete Algorithms 6(2):299\u2013312","journal-title":"Journal of Discrete Algorithms"},{"issue":"3","key":"1422_CR10","doi-asserted-by":"publisher","first-page":"2147","DOI":"10.1016\/S0304-3975(02)00577-7","volume":"290","author":"G Steiner","year":"2003","unstructured":"Steiner G (2003) On the k-path partition of graphs. Theoret Comput Sci 290(3):2147\u20132155","journal-title":"Theoret Comput Sci"},{"key":"1422_CR11","doi-asserted-by":"crossref","unstructured":"Zhao J, Xiao M (2024a) Improved approximation algorithms for cycle and path packings, in: Proceedings of the International Conference and Workshops on Algorithms and Computation, pp. 179\u2013193","DOI":"10.1007\/978-981-97-0566-5_14"},{"key":"1422_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2024.114699","volume":"1010","author":"J Zhao","year":"2024","unstructured":"Zhao J, Xiao M (2024b) A deterministic approximation algorithm for metric triangle packing. Theoret Comput Sci 1010:114699","journal-title":"Theoret Comput Sci"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-026-01422-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-026-01422-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-026-01422-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T16:17:20Z","timestamp":1784737040000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-026-01422-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,18]]},"references-count":12,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2026,7]]}},"alternative-id":["1422"],"URL":"https:\/\/doi.org\/10.1007\/s10878-026-01422-7","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"value":"1382-6905","type":"print"},{"value":"1573-2886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,18]]},"assertion":[{"value":"13 December 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 May 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 May 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","label":"Conflict of Interest","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"48"}}