{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T20:29:32Z","timestamp":1649190572091},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[1993,12]]},"abstract":"<jats:p> In this paper we study the fault-tolerant properties of the Supercube, a new inter-connection network recently introduced by Sen [15]. The Supercube is a generalization of the Hypercube that can be realized for any number of nodes and not only for powers of 2. Moreover, it has the same diameter and connectivity of the Hypercube. <\/jats:p><jats:p> We shall prove that the diameter of the surviving route graph of the N-node Supercube S<jats:sub>N<\/jats:sub>, if less than [ log <jats:sub>2<\/jats:sub> N] nodes or edges fail, is at most 4 for any minimal routing, and exhibit a minimal routing for which the surviving route graph has diameter 2. Then, we will show that, when 2<jats:sup>s<\/jats:sup>+2<jats:sup>s\u22121<\/jats:sup>\u2264N&lt;2<jats:sup>s+1<\/jats:sup> the failures are [log<jats:sub>2<\/jats:sub> N], the diameter of the surviving route graph is at most 5 for any minimal routing. <\/jats:p><jats:p> We will also prove that the fault diameter of S<jats:sub>N<\/jats:sub> is exactly [ log <jats:sub>2<\/jats:sub> N]+1 when N\u2209{2<jats:sup>s+1<\/jats:sup>\u22121, 2<jats:sup>s+1<\/jats:sup>\u22122, 2<jats:sup>s<\/jats:sup>+2<jats:sup>s\u22121<\/jats:sup>+1} and [ log <jats:sub>2<\/jats:sub> N]+2 otherwise. <\/jats:p>","DOI":"10.1142\/s0129626493000435","type":"journal-article","created":{"date-parts":[[2004,11,22]],"date-time":"2004-11-22T22:29:30Z","timestamp":1101162570000},"page":"393-405","source":"Crossref","is-referenced-by-count":6,"title":["FAULT TOLERANT ROUTING IN THE SUPERCUBE"],"prefix":"10.1142","volume":"03","author":[{"given":"VINCENZO","family":"AULETTA","sequence":"first","affiliation":[{"name":"Dipartimento di Informatica ed Applicazioni,  Un\u00edvers\u00edt\u00e0, di Salerno,  84081 Baronissi (SA), Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ADELE ANNA","family":"RESCIGNO","sequence":"additional","affiliation":[{"name":"Dipartimento di Informatica ed Applicazioni,  Un\u00edvers\u00edt\u00e0, di Salerno,  84081 Baronissi (SA), Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VITTORIO","family":"SCARANO","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Massachusetts at Amherst, Amherst, MA 01003, U.S.A."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626493000435","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:18:21Z","timestamp":1565093901000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626493000435"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,12]]},"references-count":0,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[1993,12]]}},"alternative-id":["10.1142\/S0129626493000435"],"URL":"https:\/\/doi.org\/10.1142\/s0129626493000435","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"value":"0129-6264","type":"print"},{"value":"1793-642X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,12]]}}}