{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T12:34:54Z","timestamp":1768912494390,"version":"3.49.0"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T00:00:00Z","timestamp":1719792000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T00:00:00Z","timestamp":1719792000000},"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":["11701363"],"award-info":[{"award-number":["11701363"]}],"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":[[2024,7]]},"DOI":"10.1007\/s10878-024-01190-2","type":"journal-article","created":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T18:02:22Z","timestamp":1720029742000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Approximation algorithms for two clustered arc routing problems"],"prefix":"10.1007","volume":"47","author":[{"given":"Xiaoguang","family":"Bao","sequence":"first","affiliation":[]},{"given":"Xinhao","family":"Ni","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,3]]},"reference":[{"issue":"2","key":"1190_CR1","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.orl.2021.01.017","volume":"49","author":"VA Afanasev","year":"2021","unstructured":"Afanasev VA, van Bevern R, Tsidulko OY (2021) The hierarchical Chinese postman problem: the slightest disorder makes it hard, yet disconnectedness is manageable. Oper Res Lett 49(2):270\u2013277","journal-title":"Oper Res Lett"},{"issue":"3","key":"1190_CR2","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1287\/trsc.1090.0270","volume":"43","author":"J Ar\u00e1oz","year":"2009","unstructured":"Ar\u00e1oz J, Fern\u00e1ndez E, Franquesa C (2009) The clustered prize-collecting arc routing problem. Transp Sci 43(3):287\u2013300","journal-title":"Transp Sci"},{"issue":"3","key":"1190_CR3","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1007\/s11750-017-0437-4","volume":"25","author":"J Ar\u00e1oz","year":"2017","unstructured":"Ar\u00e1oz J, Fern\u00e1ndez E, Franquesa C (2017) The generalized arc routing problem. TOP 25(3):497\u2013525","journal-title":"TOP"},{"key":"1190_CR4","unstructured":"Christofides N (1976) Worst-case analysis of a new heuristic for the travelling salesman problem. Technical Report 388. Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh"},{"issue":"6","key":"1190_CR5","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1016\/0305-0483(73)90089-3","volume":"1","author":"N Christofides","year":"1973","unstructured":"Christofides N (1973) The optimum traversal of a graph. Omega 1(6):719\u2013732","journal-title":"Omega"},{"issue":"2","key":"1190_CR6","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1287\/trsc.2016.0686","volume":"51","author":"M Colombi","year":"2017","unstructured":"Colombi M, Corber\u00e1n \u00c1, Mansini R, Plana I, Sanchis JM (2017) The hierarchical mixed rural postman problem. Transp Sci 51(2):755\u2013770","journal-title":"Transp Sci"},{"issue":"1","key":"1190_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2016.07.026","volume":"257","author":"M Colombi","year":"2017","unstructured":"Colombi M, Corber\u00e1n \u00c1, Mansini R, Plana I, Sanchis JM (2017) The hierarchical mixed rural postman problem: polyhedral analysis and a branch-and-cut algorithm. Eur J Oper Res 257(1):1\u201312","journal-title":"Eur J Oper Res"},{"key":"1190_CR8","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611973679","volume-title":"Arc routing: problems, methods, and applications","author":"\u00c1 Corber\u00e1n","year":"2015","unstructured":"Corber\u00e1n \u00c1, Laporte G (2015) Arc routing: problems, methods, and applications. SIAM, Philadelphia"},{"key":"1190_CR9","unstructured":"Drexl M (2007) On the generalized directed rural postman problem. Ph.D. thesis. Aachen University, Aachen"},{"issue":"8","key":"1190_CR10","doi-asserted-by":"publisher","first-page":"1143","DOI":"10.1057\/jors.2013.60","volume":"65","author":"M Drexl","year":"2014","unstructured":"Drexl M (2014) On the generalized directed rural postman problem. J Oper Res Soc 65(8):1143\u20131154","journal-title":"J Oper Res Soc"},{"issue":"2","key":"1190_CR11","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1287\/trsc.31.2.187","volume":"31","author":"M Dror","year":"1997","unstructured":"Dror M, Langevin A (1997) A generalized traveling salesman problem approach to the directed clustered rural postman problem. Transp Sci 31(2):187\u2013192","journal-title":"Transp Sci"},{"issue":"3","key":"1190_CR12","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1002\/net.3230170304","volume":"17","author":"M Dror","year":"1987","unstructured":"Dror M, Stern H, Trudeau P (1987) Postman tour on a graph with precedence relation on arcs. Networks 17(3):283\u2013294","journal-title":"Networks"},{"key":"1190_CR13","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1007\/BF01580113","volume":"5","author":"J Edmonds","year":"1973","unstructured":"Edmonds J, Johnson EL (1973) Matching, Euler tours and the Chinese postman. Math Program 5:88\u2013124","journal-title":"Math Program"},{"issue":"3","key":"1190_CR14","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1287\/opre.43.3.399","volume":"43","author":"HA Eiselt","year":"1995","unstructured":"Eiselt HA, Gendreau M, Laporte G (1995) Arc routing problems, part II: the rural postman problem. Oper Res 43(3):399\u2013414","journal-title":"Oper Res"},{"issue":"3","key":"1190_CR15","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1145\/322139.322150","volume":"26","author":"GN Frederickson","year":"1979","unstructured":"Frederickson GN (1979) Approximation algorithms for some postman problems. J ACM 26(3):538\u2013554","journal-title":"J ACM"},{"key":"1190_CR16","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1137\/0207017","volume":"7","author":"GN Frederickson","year":"1978","unstructured":"Frederickson GN, Hecht MS, Kim CE (1978) Approximation algorithms for some routing problems. SIAM J Comput 7:178\u2013193","journal-title":"SIAM J Comput"},{"issue":"1","key":"1190_CR17","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/S0167-6377(99)00046-2","volume":"26","author":"G Ghiani","year":"2000","unstructured":"Ghiani G, Improta G (2000) An algorithm for the hierarchical Chinese postman problem. Oper Res Lett 26(1):27\u201332","journal-title":"Oper Res Lett"},{"issue":"1","key":"1190_CR18","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.ejor.2004.06.003","volume":"169","author":"P Korteweg","year":"2006","unstructured":"Korteweg P, Volgenant T (2006) On the hierarchical Chinese postman problem with linear ordered classes. Eur J Oper Res 169(1):41\u201352","journal-title":"Eur J Oper Res"},{"key":"1190_CR19","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1002\/net.3230060305","volume":"6","author":"JK Lenstra","year":"1976","unstructured":"Lenstra JK, Rinnooy Kan AHG (1976) On general routing problems. Networks 6:273\u2013280","journal-title":"Networks"},{"issue":"1","key":"1190_CR20","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1287\/trsc.1070.0195","volume":"42","author":"N Perrier","year":"2008","unstructured":"Perrier N, Langevin A, Amaya CA (2008) Vehicle routing for urban snow plowing operations. Transp Sci 42(1):44\u201356","journal-title":"Transp Sci"},{"key":"1190_CR21","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1137\/1.9781611973679.ch2","volume-title":"Arc routing: problems, methods, and applications","author":"R van Bevern","year":"2015","unstructured":"van Bevern R, Niedermeier R, Sorge M, Weller M (2015) Complexity of arc routing problems. In: Corberan A, Laporte G (eds) Arc routing: problems, methods, and applications. SIAM, Philadelphia, pp 19\u201352"},{"issue":"4","key":"1190_CR22","doi-asserted-by":"publisher","first-page":"2499","DOI":"10.1007\/s10878-021-00772-8","volume":"44","author":"X Zhang","year":"2021","unstructured":"Zhang X, Du D, Gutin G, Ming Q, Sun J (2021) Approximation algorithms with constant ratio for general cluster routing problems. J Comb Optim 44(4):2499\u20132514","journal-title":"J Comb Optim"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-024-01190-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-024-01190-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-024-01190-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,22]],"date-time":"2024-07-22T14:42:00Z","timestamp":1721659320000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-024-01190-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7]]},"references-count":22,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,7]]}},"alternative-id":["1190"],"URL":"https:\/\/doi.org\/10.1007\/s10878-024-01190-2","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"value":"1382-6905","type":"print"},{"value":"1573-2886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7]]},"assertion":[{"value":"4 June 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 July 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"88"}}