Boolean Routing on High Degree Chordal Ring Networks

Over the past twenty-five years, the telecommunication field has evolved rapidly. Telephone and computer networks, now nearly ubiquitous, provide access to voice, data and video services throughout the world. As networking technologies evolve and proliferate, researchers develop new traffic routing strategies. The problem of routing in a distributed system has been investigated and issues concerning Boolean routing schemes have been considered. All compact routing techniques minimise time and space complexity. A good routing algorithm optimises the time and space complexity and a routing algorithm that has O(1) time complexity and O(log n) space complexity for high degree chordal ring has been found. A Boolean Routing Scheme (BRS) has been applied on ring topology and regular chordal ring of degree three. It was found that the regular chordal ring of degree three can be represented geometrically. the regular chordal ring of degree three has been categorised into two categories; the first is the regular chordal ring of degree three that satisfies the following formula n mod 4 = 0 and the second other is n mod 4≠0, where n is the number of nodes that the graph contains. A BRS that requires O(log n) bits of storage at each node, O(1) time complexity to compute a shortest path to any destination for the regular chordal ring of degree three and Ө(log n) bits of storage at each node. O(1) time complexity to compute a shortest path to any destination for the ring topologies has been shown. The BRS has been applied on chordal ring of degree six. it has been found that the chordal ring of degree six can be represented geometrically and the representation would be in three dimensions (in the space). Very little is known about routing on high degree chordal rings. A BRS that requires O(log n) bits of storage at each node ,and 0(1) time complexity to compute a shortest path to any destination for the chordal ring of degree six topologyhas been shown. The chordal ring 0(27;9;3) has been considered as a case to apply BRS

Nested tandem repeat computation and analysis : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Computational Biology at Massey University

Biological sequences have long been known to contain many classes of repeats. The most studied repetitive structure is the tandem repeat where many approximate copies of a common segment (the motif ) appear consecutively. In this thesis, a complex repetitive structure is investigated. This repetitive structure is called a nested tandem repeat. It consists of many approximate copies of two motifs interspersed with one another. This thesis is a collection of published and in progress papers. Each paper addresses a computational problem related to the analysis of nested tandem repeats. Nested tandem repeats have been observed in the intergenic spacer of the ribosomal DNA gene in Colocasia esculenta. The question of whether such repeats can be found elsewhere in biological sequence databases is addressed and NTRFinder, a software tool to detect nested tandem repeats, is described. Another problem that arises after detecting a nested tandem repeat is the alignment of the nested tandem repeat region against its two motifs. An algorithm that guarantees an optimal solution to this problem is introduced. After detecting nested tandem repeats and identifying their structures, the identification of the motif boundaries is an unsolved problem which arises not only in nested tandem repeats but in tandem repeats as well. Heuristic solutions to this problem are implemented and tested. In order to compare two tandem repeat sequences an algorithm that aligns a hypothetical ancestral sequence of both sequences against each sequence is presented. This algorithm considers substitutions, deletions, and unidirectional duplication, namely, from ancestor to descendant

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