{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:50:37Z","timestamp":1759063837915},"reference-count":6,"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":4607,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1994,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For a given connected graph <jats:italic>G<\/jats:italic> of order <jats:italic>n<\/jats:italic>, a routing <jats:italic>R<\/jats:italic> is a set of <jats:italic>n<\/jats:italic>(<jats:italic>n<\/jats:italic> \u2010 1) simple paths <jats:italic>R<\/jats:italic>(<jats:italic>x, y<\/jats:italic>) specified for every ordered pair (<jats:italic>x, y<\/jats:italic>) of vertices in <jats:italic>G<\/jats:italic>. A routing <jats:italic>R<\/jats:italic> is consistent if for every vertex <jats:italic>z<\/jats:italic> on <jats:italic>R<\/jats:italic>(<jats:italic>x, y<\/jats:italic>) the paths <jats:italic>R<\/jats:italic>(<jats:italic>x, z<\/jats:italic>) and <jats:italic>R<\/jats:italic>(<jats:italic>z, y<\/jats:italic>) are induced by <jats:italic>R<\/jats:italic>(<jats:italic>x, y<\/jats:italic>). A network is defined by an ordered pair (<jats:italic>G, R<\/jats:italic>), where <jats:italic>G<\/jats:italic> is a connected graph and <jats:italic>R<\/jats:italic> is a routing of <jats:italic>G<\/jats:italic>. The vertex\u2010forwarding index \u03b6(<jats:italic>G, R<\/jats:italic>) of a network (<jats:italic>G, R<\/jats:italic>) is the maximum number of paths of <jats:italic>R<\/jats:italic> passing through any vertex of <jats:italic>G<\/jats:italic>. The minimum of \u03b6(<jats:italic>G, R<\/jats:italic>) over all possible routings of a connected graph <jats:italic>G<\/jats:italic> is denoted by \u03b6(<jats:italic>G<\/jats:italic>). Similarly, the notion of the edge\u2010forwarding index of a network can be defined. In this paper, we prove that, in general, the vertex\u2010forwarding index cannot be obtained by taking the minimum of \u03b6(<jats:italic>G, R<\/jats:italic>) over all possible consistent routings of <jats:italic>G<\/jats:italic>. However, this can be done for the class of Cayley graphs. We prove for a specific class of routings that the computation of \u03b6(<jats:italic>G<\/jats:italic>) is NP\u2010complete for graphs of diameter at least 4 and is polynomial for graphs of diameter 2. Similar problems are studied for the edge\u2010forwarding index. \u00a9 1994 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/net.3230240204","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T17:21:59Z","timestamp":1178990519000},"page":"75-82","source":"Crossref","is-referenced-by-count":18,"title":["Forwarding indices of consistent routings and their complexity"],"prefix":"10.1002","volume":"24","author":[{"given":"M. C.","family":"Heydemann","sequence":"first","affiliation":[]},{"given":"J. C.","family":"Meyer","sequence":"additional","affiliation":[]},{"given":"D.","family":"Sotteau","sequence":"additional","affiliation":[]},{"given":"J.","family":"Opatrny","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graphs and Hypergraphs","author":"Berge C.","year":"1973"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1987.1057290"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400875184"},{"key":"e_1_2_1_5_2","volume-title":"Computers and Intractability. A Guide to Theory of NP\u2010Completeness","author":"Garey M. R.","year":"1979"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(89)90022-X"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1137\/0406033"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230240204","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230240204","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T14:38:52Z","timestamp":1698158332000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230240204"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,3]]},"references-count":6,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1994,3]]}},"alternative-id":["10.1002\/net.3230240204"],"URL":"https:\/\/doi.org\/10.1002\/net.3230240204","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,3]]}}}