Set-to-Set Disjoint-Path Routing in Metacube

Abstract

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 $2^{2^km+k}$ 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, $\node {s}_i\rightarrow \node {t}_j,~1\leq i,j \leq m+k, \node{s}_i\in S, \node{t}_j\in T$, in $O((m+k)(2^km)\log (m+k))$ time. The length of the paths is at most $(m+1)2^k+(2k+1)(\lceil \lg (m+k)\rceil +\lfloor \lg 2(m+k)\rfloor +1)$ if ($k=2$ and $m\geq 3$) or ($k=3$ and $m\geq 2)$ or ($k>3$). In other cases, the length of the paths is at most $(k+1)(m2^k+m+k)$.