An efficient algorithm for k-pairwise disjoint paths in star graphs

Abstract

In this paper, we give an efficient algorithm for the following problem in the n-dimensional star graph G n : Given k = ⌈( n − l) 2 ⌉ pairs of distinct nodes ( s 1, t 1),…,( s k , t k ) in G n , find k node-disjoint paths S i → t i , 1 ⩽ i ⩽ k. Our algorithm finds the k disjoint paths of length at most d( G n ) + 5 in O( n 2) optimal time, where d(G n) = ⌊3( n − 1) 2 ⌋ is the diameter of G n . This improves the previous results of 4( n − 2) (path length) and O( n 4 log n) (time), respectively.