Nearly optimal one-to-many parallel routing in star networks

Star networks were proposed recently as an attractive alternative to the well-known hypercube models for interconnection networks. Extensive research has been performed that shows that star networks are as versatile as hypercubes. This paper is an effort in the same direction. Based on the well-known paradigms, we study the one-to-many parallel routing problem on star networks and develop an improved routing algorithm that finds n-1 node-disjoint paths between one node and a set of other n-1 nodes in the n-star network. These parallel paths are proven of minimum length within a small additive constant, and the running time of our algorithm is bounded by O(n²). More specifically, given a node s and n-1 other nodes {t₁, t₂ , …, t_n-1} in the n-star network, our algorithm constructs n-1 node-disjoint paths P₁, P₂, …, P_n-1, where P_i is a path from s to t_j of length at most dist(s, t_j)+6 and dist(s, t _j) is the distance, i.e., the length of a shortest path, from s to t_j, for i=1, 2, …, n-1.The best bound on the path length by previously known algorithms for the same problem is 5(n-2)≈10Δ_n/3, where Δ_n=max{dist(s, t)} is the diameter of the n-star network