A Node-to-Set Disjoint-Path Routing Algorithm in Metacube

The metacube (MC) was introduced as a topology for interconnection networks of large parallel computers, and it has a merit that with a diameter similar to that of the hypercube, its degree is much lower: the 2^{m2k + k} nodes of a metacube MC(k, m) have a degree of to + k. We introduce in this paper an efficient routing algorithm for finding in a metacube MC(k, m) disjoint paths between one source node and a maximum of m + k target nodes. We show that for any source node s, and any target nodes T = {t₁,..., t_n}, n ¿ m + k, we can find n disjoint paths from s to t_i (1 ¿ i < n) of maximal length km2^k + m2^k + 3k + 4 in O(nm2^k) time.