{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T11:09:29Z","timestamp":1781003369268,"version":"3.54.1"},"reference-count":17,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4058,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1995,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The symmetric Generalized Traveling Salesman Problem (GTSP) is a variant of the classical symmetric Traveling Salesman Problem, in which the nodes are partitioned into clusters and the salesman has to visit at least one node for each cluster. A different version of the problem, called E\u2010GTSP, arises when exactly one node for each cluster has to be visited. Both GTSP and E\u2010GTSP are <jats:italic>NP<\/jats:italic>\u2010hard problems and find practical applications in routing, scheduling, and location\u2010routing. in this paper, we model GTSP and E\u2010GTSP as integer linear programs and study the facial structure of the corresponding polytopes. in a companion paper, Theresults described in this work have been used to design a branch\u2010and\u2010cut algorithm for the exact solution of instances up to 442 nodes.<\/jats:p>","DOI":"10.1002\/net.3230260206","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T20:21:56Z","timestamp":1179001316000},"page":"113-123","source":"Crossref","is-referenced-by-count":85,"title":["The symmetric generalized traveling salesman polytope"],"prefix":"10.1002","volume":"26","author":[{"given":"Matteo","family":"Fischetti","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Juan Jos\u00e9 Salazar","family":"Gonz\u00e1lez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paolo","family":"Toth","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230190602"},{"key":"e_1_2_1_3_2","unstructured":"E.Balas The prize collecting traveling salesman problem: II. Polyhedral results. Working paper Carnegie Mellon University (July1993)."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.17.4.1001"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581274"},{"key":"e_1_2_1_6_2","unstructured":"M.Fischetti J. J.SalazarandP.Toth A branch\u2010and\u2010cut algorithm for the symmetric generalized travelling salesman problem. Working paper University of Bologna (November 1993)."},{"key":"e_1_2_1_7_2","unstructured":"M.Fischetti andP.Toth An additive approach for the optimal solution of the prize\u2010collecting travelling salesman problem. Vehicle Routing: Methods and Studies (B. L. Golden and A. A. Assad Eds.). 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University of Tennessee (1988)."},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.39.4.623"},{"key":"e_1_2_1_15_2","first-page":"39","article-title":"An efficient transformation of the generalized traveling salesman problem","volume":"31","author":"Noon C. E.","year":"1993","journal-title":"INFOR"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.23.4.833"},{"key":"e_1_2_1_17_2","unstructured":"J. J.Salazar Algoritmi per il problema del Commesso Viaggiatore Generalizzato. PhD Dissertation Royal Spanish College in Bologna Italy (1992)."},{"key":"e_1_2_1_18_2","unstructured":"M. M.Sepehri The symmetric generalized travelling salesman problem. PhD Dissertation University of Tennessee Knoxville (1991)."}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230260206","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230260206","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T02:48:20Z","timestamp":1698288500000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230260206"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,9]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,9]]}},"alternative-id":["10.1002\/net.3230260206"],"URL":"https:\/\/doi.org\/10.1002\/net.3230260206","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,9]]}}}