Abstract
A graph G(V, E) (|V|⩾2k) satisfies property Ak if, given k pairs of distinct nodes (s1, t1), …, (sk, tk) of V(G), there are k mutually node-disjoint paths, one connecting si and ti for each i, 1⩽i⩽k. A necessary condition for any graph to satisfy Ak is that it is (2k−1)-connected. Hypercubes are important interconnection topologies for parallel computation and communication networks. It has been known that hypercubes of dimension n (which are n-connected) satisfy A⌈n/2⌉. In this paper we give an algorithm which, given k=⌈n/2⌉ pairs of distinct nodes (s1, t1), …, (sk, tk) in the n-dimensional hypercube, finds the k disjoint paths of length at most n+⌈logn⌉+1 in O(n2log*n) time.
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