Date of Award

2000

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical and Computer Engineering

First Advisor

Ramachandran Vaidyanathan

Abstract

Multiple bus networks (MBN) connect processors via buses. This dissertation addresses issues related to running binary-tree algorithms on MBNs. These algorithms are of a fundamental nature, and reduce inputs at leaves of a binary tree to a result at the root. We study the relationships between running time, degree (maximum number of connections per processor) and loading (maximum number of connections per bus). We also investigate fault-tolerance, meshes enhanced with MBNs, and VLSI layouts for binary-tree MBNs. We prove that the loading of optimal-time, degree-2, binary-tree MBNs is non-constant. In establishing this result, we derive three loading lower bounds Wn , W&parl0;n23&parr0; and W&parl0;nlogn&parr0; , each tighter than the previous one. We also show that if the degree is increased to 3, then the loading can be a constant. A constant loading degree-2 MBN exists, if the algorithm is allowed to run slower than the optimal. We introduce a new enhanced mesh architecture (employing binary-tree MBNs) that captures features of all existing enhanced meshes. This architecture is more flexible, allowing all existing enhanced mesh results to be ported to a more implementable platform. We present two methods for imparting tolerance to bus and processor faults in binary-tree MBNs. One of the methods is general, and can be used with any MBN and for both processor and bus faults. A key feature of this method is that it permits the network designer to designate a set of buses as "unimportant" and consider all faulty buses as unimportant. This minimizes the impact of faulty elements on the MBN. The second method is specific to bus faults in binary-tree MBNs, whose features it exploits to produce faster solutions. We also derive a series of results that distill the lower bound on the perimeter layout area of optimal-time, binary-tree MBNs to a single conjecture. Based on this we believe that optimal-time, binary-tree MBNs require no less area than a balanced tree topology even though such MBNs can reuse buses over various steps of the algorithm.

ISBN

9780599853133

Pages

148

DOI

10.31390/gradschool_disstheses.7190

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