{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T08:31:33Z","timestamp":1759048293507},"reference-count":32,"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":6068,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1990,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider two cost allocation problems that arise when the prospective users of a communication network seek a fair method for allocating the cost of constructing the network. We assume the network is of minimum cost and its edge capacities are large enough to satisfy requirements for every pair of users. If the requirements are time\u2010invariant and have to be satisfied simultaneously, the problem of finding a minimum\u2010cost network is called the <jats:italic>simultaneous network synthesis problem<\/jats:italic>, whereas if the requirements can be satisfied for one pair of users at a time, it is called the nonsimultaneous network synthesis problem. We formulate the cost allocation problems arising from the above problems as cooperative games, referred to as the simultaneous and the nonsimultaneous network synthesis games. We prove that both the (equal cost) nonsimultaneous and the simultaneous network synthesis games are convex and provide nonredundant representations of their cores. For the simultaneous network synthesis game, we present a closed\u2010form expression for the nucleolus and prove that it coincides with the Shapley value. For the (equal cost) nonsimultaneous network synthesis game, we, provide a closed\u2010form expression for the nucleolus when the requirement structure is tree\u2010shaped and develop a quadratic time algorithm for computing the Shapley value in this case.<\/jats:p>","DOI":"10.1002\/net.3230200207","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T08:49:29Z","timestamp":1178959769000},"page":"209-229","source":"Crossref","is-referenced-by-count":13,"title":["On cost allocation in communication networks"],"prefix":"10.1002","volume":"20","author":[{"given":"Daniel","family":"Granot","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mehran","family":"Hojati","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"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.3230060404"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0038-0121(73)90029-3"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800120303"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02591996"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1137\/0109047"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1137\/0110020"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1137\/0112029"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580585"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.35.2.234"},{"key":"e_1_2_1_12_2","volume-title":"On some network flow games. Working Paper No. 1056","author":"Granot D.","year":"1984"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01584227"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02592000"},{"key":"e_1_2_1_15_2","unstructured":"M.Hojati The network synthesis problem: Cost allocations and algorithms. Ph. D. Thesis Faculty of Commerce and Business Administration University of British Columbia (October 1987)."},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.7.3.476"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.30.5.998"},{"key":"e_1_2_1_18_2","volume-title":"Computation of the kernels of simple games and the nucleolus of N\u2010person games. Research Memorandum No. 31","author":"Kopelowitz A.","year":"1967"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01766216"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01753435"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.4.4.303"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.3.3.189"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230080104"},{"key":"e_1_2_1_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01681356"},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.9.2.309"},{"key":"e_1_2_1_26_2","doi-asserted-by":"publisher","DOI":"10.1137\/0117107"},{"key":"e_1_2_1_27_2","first-page":"307","article-title":"A value for n\u2010person games","volume":"23","author":"Shapley L. S.","year":"1953","journal-title":"Ann. Math. Study"},{"key":"e_1_2_1_28_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01753431"},{"key":"e_1_2_1_29_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01753437"},{"key":"e_1_2_1_30_2","volume-title":"On the core of cost allocation games defined on location problems","author":"Tamir A.","year":"1980"},{"key":"e_1_2_1_31_2","volume-title":"On the core of network synthesis games. 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