Set-to-Set Disjoint-Path Routing in Metacube

In this paper, we propose an efficient algorithm that finds disjoint paths for set-to-set disjoint-paths routing in metacube. Metacube is a cluster-based, hypercube-like interconnection network that can connect a huge number of nodes with small amount of links per node. An metacube MC(k, m) has 2^2km+k nodes and m + k links per node. For an MC(k, m) and two sets of nodes S and T of size m+k, the algorithm finds m + k disjoint paths, s_i → t_j, 1 ≤ i, j ≤ m + k, s_i ∈ S,t_j ∈ T, in O((m + k)(2^k m) log(m + k)) time. The length of the paths is at most (m + 1)2^k + (2k + 1)(⌈1g(m + k)⌉ + ⌊1g 2(m + k)⌋ +1) if (k = 2 and m ≥ 3) or (k = 3 and m ≥ 2) or (k >; 3). In other cases, the length of the paths is at most (k + 1)(m2^k + m + k).