Issue No. 12 - December (1997 vol. 8)

ISSN: 1045-9219

pp: 1196-1202

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.640011

ABSTRACT

<p><b>Abstract</b>—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 <it>n</it>− 1 node-disjoint paths between one node and a set of other <it>n</it>− 1 nodes in the <it>n</it>-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 <it>O</it>(<it>n</it><super>2</super>). More specifically, given a node <it>s</it> and <it>n</it>− 1 other nodes {<it>t</it><sub>1</sub>, <it>t</it><sub>2</sub>, ..., <it>t</it><sub><it>n</it>-1</sub>} in the <it>n</it>-star network, our algorithm constructs <it>n</it>− 1 node-disjoint paths <it>P</it><sub>1</sub>, <it>P</it><sub>2</sub>, ..., <it>P</it><sub><it>n</it>-1</sub>, where <it>P</it><sub><it>i</it></sub> is a path from <it>s</it> to <it>t</it><sub><it>i</it></sub> of length at most <it>dist</it>(<it>s</it>, <it>t</it><sub><it>i</it></sub>) + 6 and <it>dist</it>(<it>s</it>, <it>t</it><sub><it>i</it></sub>) is the distance, i.e., the length of a shortest path, from <it>s</it> to <it>t</it><sub><it>i</it></sub>, for <it>i</it> = 1, 2, ..., <it>n</it>− 1. The best bound on the path length by previously known algorithms for the same problem is <tmath>$5(n - 2) \approx 10\Delta_n/3,$</tmath> where Δ<sub><it>n</it></sub> = max{<it>dist</it>(<it>s</it>, <it>t</it>)} is the diameter of the <it>n</it>-star network.</p>

INDEX TERMS

Interconnection network, node-disjoint paths, parallel routing, routing algorithm, shortest path, star network.

CITATION

Jianer Chen, Chi-Chang Chen, "Nearly Optimal One-to-Many Parallel Routing in Star Networks",

*IEEE Transactions on Parallel & Distributed Systems*, vol. 8, no. , pp. 1196-1202, December 1997, doi:10.1109/71.640011