Communication in Chordal Ring Networks

The chordal ring networks have been the objects of a great deal of attention in recent years, and several parallel computers have configurations based on the chordal ring topology. Common ways to improve the network performance are to increase its connectivity and decrease its diameter. Therefore, this thesis addresses the fundamental problems of communication in chordal ring of high degree and studies the degree diameter problem in such topology. In particular, we concentrate on Compact Routing, a family of routing methods that minimizes the space and time complexity. An effecient boolean routing scheme that has O(1) time complexity and O(log n) space complexity is introduced. Based on the existing results in [61] done by Narayanan and Opatrny, we propose a new algorithm for some families of chordal ring of degree six graphs. New properties for this families of graphs have been introduced such as finding the maximum number of nodes for a given diameter; it has been found that the chordal ring that has the maximum number of nodes for diameter k is G(4k2 + 2k + 1; 2k + 1; 2k2). Moreover, a broadcasting scheme for this family of chordal rings of degree six has been constructed. It has been found that this scheme can broadcast the message to all nodes in the graph by time at most k + 3 where k is the diameter. The uniqueness property of the shortest path type between any two nodes in chordal rings of degree four and six has been introduced, this property helps us in deriving our results.

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