An efficient algorithm for k-pairwise node disjoint path problem in hypercubes

In this paper, we give an efficient algorithm for the following k-pairwise node disjoint path problem in n-dimensional hypercubes H/sub n/: Given k=[n/2] pairs of 2k distinct nodes (s/sub 1/, t/sub 1/), ..., (s/sub k/, t/sub k/) in H/sub n/, n/spl ges/4, find k node disjoint paths s/sub i//spl rarr/t/sub i/, 1/spl les/i/spl les/k. Our algorithm finds the k node disjoint paths in O(n/sup 2/ log* n) time which improves the previous result of O(n/sup 2/ log n). The length of the paths constructed in our algorithm is at most n+[log n]+1 which improves the previous result of 2n as well. The result of this paper shows that the k-pair-diameter d/sup P//sub [n/2]/(/sub H/n) of H/sub n/ satisfies d/sup P//sub [n/2]/(H/sub n/)/spl les/n+[log n]+1.