Edge-disjoint spanning trees for the generalized butterfly networks and their applications

The generalized butterfly GBN(d,n) has recently gained some interest as a point-to-point interconnection network rather than the well known multi-stage butterfly networks. We construct edges-disjoint spanning trees (abbreviated EDSTs) for the GBN(d,n). Our construction is based on the decomposition of the GBN(d,n) into dn vertex-disjoint cycles of length n. As an application, we propose an efficient broadcasting algorithm and its fault-tolerant version for the GBN(d,n). Our fault-tolerant broadcasting algorithm is optimal in terms of fault-tolerance, because it resists 2d-1 edge failures (2d is the degree of the GBN(d,n)). We also propose an efficient scattering algorithm and its fault-tolerant version which resists 2d-3 edge faults.