Fault Tolerant Routing in the Supercube 1. Introduction - CiteSeerX
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Fault Tolerant Routing in the Supercube 1. Introduction - CiteSeerX
since just 1 edge is necessary to connect u and u. Otherwise, (u;v) = s ? 1 and the only fault free neighbor of u (risp. v) has distance s from v (risp. u) in V2. V3.
Parallel Processing Letters
c World Scienti c Publishing Company
Fault Tolerant Routing in the Supercube VINCENZO AULETTA and ADELE ANNA RESCIGNO Dipartimento di Informatica ed Applicazioni Universita di Salerno 84081 Baronissi (SA) { Italy VITTORIO SCARANO Department of Computer Science University of Massachusetts at Amherst Amherst, MA 01003, U.S.A. ABSTRACT In this paper we study the fault{tolerant properties of the Supercube, a new interconnection 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. We prove that the diameter of the surviving route graph of the {node Supercube N , if less than blog2 c 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 show that, when 2s + 2s?1 2s+1 and the failures are dlog2 e, the diameter of the surviving route graph is at most 5 for any minimal routing. We also prove that the fault diameter of N is exactly blog2 c + 1 when 62 f2s+1 ? 1 2s+1 ? 2 2s + 2s?1 + 1g, and blog2 c + 2 otherwise. N
