Node-to-set disjoint paths problem in star graphs

Abstract

Given a node s and a set T = t 1,…, t k of k nodes in a k-connected graph, the node-to-set disjoint paths problem is to find k node-disjoint paths p i : s → t i , 1 ⩽ i ⩽ k. In this paper, we give two O( n 2) time algorithms for the node-to-set disjoint paths problem in n-dimensional star graphs G n which are ( n − 1)-connected. We first give a simple algorithm which finds n − 1 node-disjoint paths of length at most d( G n ) + 3, where d(G n) = ⌊ 3(n − 1) 2 ⌋ is the diameter of G n . Then, we refine the algorithm to find n − 1 node-disjoint paths of length at most d( G n ) + 2. A lower bound on the length of the paths for the above problem in G n is d( G n ) + 1.