A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Unicast-Based Multicast Communication in Wormhole-Routed Networks
IEEE Transactions on Parallel and Distributed Systems
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A star graph Sn [1], of order n, is defined to be a symmetric graph G=(V, E) where V is the set of n! vertices, each representing a distinct permutation of n elements and E is the set of symmetric edges such that two permutations (nodes) are connected by an edge iff one can be reached from the other by interchanging its first symbol with any other symbol. The star graph Sn is a (n−1)-regular graph with n! nodes and n!(n−1)/2 edges. Recursive hierarchical structure is one of the most attractive and well known properties of star graphs. A dimension n star graph can be divided into n substars of dimension n−1 by grouping the nodes with the same symbol at the ith position together, 2≤i≤n [see Figure 1]. In this paper, we propose a new recursive hierarchical structure of star graphs. The objective is to redesign shortest routing in star graphs in the light of this new structure and design new efficient algorithms for shortest path multicast algorithms [2] adaptibe to bandwidth and latency requirements.