{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:20:21Z","timestamp":1759638021601},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"03n04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[2002,9]]},"abstract":"<jats:p> Motivated by problems in telecommunication satellites, we investigate rearrangeable permutation networks made of binary switches. A simple counting argument shows that the number of switches necessary to build a n \u00d7 n rearrangeable networks (i.e. capable of realizing all one-to-one mappings of its n inputs to its n outputs) is at least \u2308 log <jats:sub>2<\/jats:sub> (n!) \u2309 = n log <jats:sub>2<\/jats:sub> n - n log <jats:sub>2<\/jats:sub> e + o(n) as n \u2192 \u221e. For n = 2<jats:sup>r<\/jats:sup>, the r-dimensional Bene\u0161 network gives a solution using [Formula: see text] switches. Waksman, and independently Goldstein and Leibholz, improved these networks using n log <jats:sub>2<\/jats:sub> n - n + 1 switches. We provide an extension of this result to arbitrary values of n, using [Formula: see text] switches. Finally the fault-tolerance issue of these networks is discussed. <\/jats:p>","DOI":"10.1142\/s0129626402000999","type":"journal-article","created":{"date-parts":[[2002,12,11]],"date-time":"2002-12-11T06:18:01Z","timestamp":1039587481000},"page":"287-296","source":"Crossref","is-referenced-by-count":20,"title":["ON ARBITRARY SIZE WAKSMAN NETWORKS AND THEIR VULNERABILITY"],"prefix":"10.1142","volume":"12","author":[{"given":"B.","family":"BEAUQUIER","sequence":"first","affiliation":[{"name":"MASCOTTE (MASCOTTE is a joint project of I3S Laboratory (C.N.R.S. and University of Nice) and INRIA.) Project, INRIA Sophia Antipolis, B.P. 93, F-06902 Sophia Antipolis Cedex, France"}]},{"given":"E.","family":"DARROT","sequence":"additional","affiliation":[{"name":"MASCOTTE (MASCOTTE is a joint project of I3S Laboratory (C.N.R.S. and University of Nice) and INRIA.) Project, INRIA Sophia Antipolis, B.P. 93, F-06902 Sophia Antipolis Cedex, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1964.tb04102.x"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1975.tb02844.x"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1953.tb01433.x"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1109\/PGEC.1967.264771"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1968.tb00063.x"},{"key":"p_10","first-page":"5","volume":"17","author":"Kautz W.","year":"1968","journal-title":"IEEE Transactions on Computers"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1145\/321439.321449"},{"key":"p_12","first-page":"3","volume":"7","author":"Chang C.","year":"1997","journal-title":"PPL"}],"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626402000999","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:18:46Z","timestamp":1565093926000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626402000999"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9]]},"references-count":8,"journal-issue":{"issue":"03n04","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2002,9]]}},"alternative-id":["10.1142\/S0129626402000999"],"URL":"https:\/\/doi.org\/10.1142\/s0129626402000999","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"value":"0129-6264","type":"print"},{"value":"1793-642X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9]]}}}