{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:19:24Z","timestamp":1740122364197,"version":"3.37.3"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T00:00:00Z","timestamp":1676851200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T00:00:00Z","timestamp":1676851200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s10878-023-00997-9","type":"journal-article","created":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T19:23:50Z","timestamp":1677007430000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The balanced 2-median and 2-maxian problems on a tree"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1397-8529","authenticated-orcid":false,"given":"Jafar","family":"Fathali","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mehdi","family":"Zaferanieh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,2,20]]},"reference":[{"key":"997_CR1","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s10479-008-0339-9","volume":"167","author":"O Berman","year":"2009","unstructured":"Berman O, Drezner Z, Tamir A, Wesolowsky GO (2009) Optimal location with equitable loads. Ann Oper Res 167:307\u2013325","journal-title":"Ann Oper Res"},{"key":"997_CR2","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1016\/j.orl.2006.03.016","volume":"35","author":"RE Burkard","year":"2007","unstructured":"Burkard RE, Fathali J, Kakhki HT (2007) The p-maxian problem on a tree. Oper Res Lett 35:331\u2013335","journal-title":"Oper Res Lett"},{"key":"997_CR3","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/S0166-218X(00)00177-3","volume":"105","author":"RE Burkard","year":"2000","unstructured":"Burkard RE, \u00c7ela E, Dollani H (2000) 2-Median in trees with pos\/neg weights. Discret Appl Math 105:51\u201371","journal-title":"Discret Appl Math"},{"key":"997_CR4","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1080\/00207543.2017.1401751","volume":"56","author":"MS Daskin","year":"2018","unstructured":"Daskin MS, Tucker EL (2018) The trade-off between the median and range of assigned demand in facility location models. Int J Prod Res 56:97\u2013119. https:\/\/doi.org\/10.1080\/00207543.2017.1401751","journal-title":"Int J Prod Res"},{"key":"997_CR5","doi-asserted-by":"crossref","unstructured":"Eiselt HA, Laporte G (1995) Objectives in location problems. In: Facility location: a survey of applications and methods. Ed.: Drezner Z. Springer, Berlin, 151-180","DOI":"10.1007\/978-1-4612-5355-6_9"},{"key":"997_CR6","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1002\/net.3230260413","volume":"26","author":"B Gavish","year":"1995","unstructured":"Gavish B, Sridhar S (1995) Computing the 2-median on tree networks is $$O(n\\log n)$$ time. Networks 26:305\u2013317","journal-title":"Networks"},{"key":"997_CR7","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1287\/opre.12.3.450","volume":"12","author":"SL Hakimi","year":"1964","unstructured":"Hakimi SL (1964) Optimum locations of switching centers and the absolute centers and medians of a graph. Oper Res 12:450\u2013459","journal-title":"Oper Res"},{"key":"997_CR8","doi-asserted-by":"publisher","first-page":"462","DOI":"10.1287\/opre.13.3.462","volume":"13","author":"SL Hakimi","year":"1965","unstructured":"Hakimi SL (1965) Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Oper Res 13:462\u2013475","journal-title":"Oper Res"},{"key":"997_CR9","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1287\/trsc.7.3.287","volume":"7","author":"GY Handler","year":"1973","unstructured":"Handler GY (1973) Minimax location of a facility in an undirected tree networks. Transp Sci 7:287\u2013293","journal-title":"Transp Sci"},{"key":"997_CR10","volume-title":"Dispersing facilities on a network","author":"P Hansen","year":"1988","unstructured":"Hansen P, Moon ID (1988) Dispersing facilities on a network. Presentation at the TIMS\/ORSA Joint National Meeting, Washington"},{"key":"997_CR11","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1137\/0137041","volume":"37","author":"O Kariv","year":"1979","unstructured":"Kariv O, Hakimi SL (1979) An algorithmic approach to network location problems Part II: p-medians. SIAM J Appl Math 37:539\u2013560","journal-title":"SIAM J Appl Math"},{"key":"997_CR12","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.ejor.2010.10.012","volume":"210","author":"A Marin","year":"2011","unstructured":"Marin A (2011) The discrete facility location problem with balanced allocation of customers. Eur J Oper Res 210:27\u201338","journal-title":"Eur J Oper Res"},{"key":"997_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0377-2217(94)90200-3","volume":"74","author":"MT Marsh","year":"1994","unstructured":"Marsh MT, Schilling DA (1994) Equity measurement in facility location analysis\u2014a review and framework. Eur J Oper Res 74:1\u201317","journal-title":"Eur J Oper Res"},{"key":"997_CR14","doi-asserted-by":"publisher","first-page":"1030","DOI":"10.1007\/s10878-020-00650-9","volume":"40","author":"TK Nguyen","year":"2020","unstructured":"Nguyen TK, Hung NT, Nguyen-Thu H (2020) A linear time algorithm for the p-maxian problem on trees with distance constraint. J Comb Optim 40:1030\u20131043. https:\/\/doi.org\/10.1007\/s10878-020-00650-9","journal-title":"J Comb Optim"},{"key":"997_CR15","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1002\/net.21978","volume":"77","author":"A Oudjit","year":"2021","unstructured":"Oudjit A, Stallmann MF (2021) Efficient algorithms for finding 2-medians of a tree. Networks 77:383\u2013402. https:\/\/doi.org\/10.1002\/net.21978","journal-title":"Networks"},{"key":"997_CR16","doi-asserted-by":"publisher","unstructured":"Schulz C, Strash D (2018) Graph partitioning: formulations and applications to big data. In: Sakr S, Zomaya A (eds). Encyclopedia of Big Data Technologies. Springer, Cham https:\/\/doi.org\/10.1007\/978-3-319-63962-8_312-2","DOI":"10.1007\/978-3-319-63962-8_312-2"},{"key":"997_CR17","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/0167-6377(96)00021-1","volume":"19","author":"A Tamir","year":"1996","unstructured":"Tamir A (1996) An $$O(pn^2)$$ algorithm for the p-median and related problems on tree graphs. Oper Res Lett 19:59\u201364","journal-title":"Oper Res Lett"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-023-00997-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-023-00997-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-023-00997-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T19:31:05Z","timestamp":1677007865000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-023-00997-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,20]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["997"],"URL":"https:\/\/doi.org\/10.1007\/s10878-023-00997-9","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"type":"print","value":"1382-6905"},{"type":"electronic","value":"1573-2886"}],"subject":[],"published":{"date-parts":[[2023,2,20]]},"assertion":[{"value":"1 February 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 February 2023","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 declared that they have no conflict of interest with any Organization\/Institute.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}}],"article-number":"69"}}