Parallel construction of optimal independent spanning trees on Cartesian product of complete graphs

A set of k spanning trees rooted at the same vertex r in a graph G is said to be independent if for each vertex x other than r, the k paths from r to x, one path in each spanning tree, are internally disjoint. Using independent spanning trees (ISTs) one can design fault-tolerant broadcasting schemes and increase message security in a network. Thus, the problem of ISTs on graphs has been received much attention. Recently, Yang et al. proposed a parallel algorithm for generating optimal ISTs on the hypercube. In this paper, we propose a similar algorithm for generating optimal ISTs on Cartesian product of complete graphs. The algorithm can be easily implemented in parallel or distributed systems. Moreover, the proof of its correctness is simpler than that of Yang et al.

Research highlights
► A parallel algorithm for constructing optimal independent spanning trees on Cartesian product of complete graphs was given.
► It was proved that the constructed Δ optimal independent spanning trees on the generalized base-b hypercube are isomorphic.