A topological property of hypercubes: node disjoint paths

Node-to-Set Disjoint Paths Problem in a Möbius Cube

“…, d k } in a k-connected graph G = (V, E), find k paths s d i (1 ≤ i ≤ k) between s and each element of D that are node-disjoint except for s. Note that in this paper the notations u v and u → v for two nodes u and v represent a path from u to v and an edge from u and v, respectively. The node-to-set disjoint paths problem is an important issue in parallel and distributed computation [5], [10], [15], [16] as well as the node-to-node disjoint paths problem [7], [12], [18], [22] and the set-to-set disjoint paths problem [3], [4], [9], [11].…”

An algorithm for disjoint paths in bubble‐sort graphs

“…In design and implementation of parallel and distributed computing systems, finding disjoint paths in interconnection networks is a fundamental issue [2,4,5,[11][12][13]. Among the problems involved is the node-to-set disjoint paths problem: Given a source node s and a set D = {d 1 , d 2 , .…”

An Efficient Algorithm for the k-Pairwise Disjoint Paths Problem in Hypercubes

“…To find the k disjoint paths is known as the k-pairwise disjoint paths problem. This problem has been investigated in both mathematical terms and interconnection network studies [2,5,7,10,11,14,16]. Whether a graph G(V, E) satisfies A k for k 2 can be verified in poly(|V| ) time [14].…”

“…A necessary condition for any graph to satisfy A k is that it is (2k&1)-connected [16]. Hypercubes of dimension n (n 4) are the first nontrivial class of n-connected graphs that satisfies A WnÂ2X [11].…”