Type of Document	Master's Thesis
Author	Sethuraman, Karthik
Author's Email Address	ksethu1@lsu.edu
URN	etd-01252005-144734
Title	Mapping Weak Multidimensional Torus Communications on Optical Slab Waveguides
Degree	Master of Science in Electrical Engineering (M.S.E.E.)
Department	Electrical & Computer Engineering
Advisory Committee	Advisor Name Title R. Vaidyanathan Committee Chair Ahmed A. El-Amawy Committee Member Jerry Trahan Committee Member
Keywords	multidimensional torus lower bounds slab waveguides optical interconnects interconnection topology
Date of Defense	2004-11-04
Availability	unrestricted
Abstract This thesis deals with the mapping of communication of a d-dimensional weak torus on an optical medium. Our results are derived in the setting of a sawtooth slab waveguide. The mapping aims to reduce the number and cost of optical components, by exploiting the fact that not all edges of a weak topology are used simultaneously. This approach allows for a better utilization of the huge bandwidth of an optical slab waveguide; currently the cost and size of optical components external to the optical communication medium are the primary bottleneck of an optical interconnect. We introduce the notion of adjacency and aggregates to model the reusability of optical components across multiple channels. We present methods to map a d-dimensional torus on the optical sawtooth slab waveguide. Specifically, for a One-dimensional torus (or ring), we propose two methods, called mixed aggregate method and the pure aggregate method, that are each nearly optimal. A special case of the pure aggregate method, called separable aggregate mapping, has the added advantage of significantly reducing the optical hardware. For a Two-dimensional torus, we propose a pure aggregate mapping method that has optimal cost where the two dimensions of the torus have relatively prime sizes. We extend this method to a general d-dimensional tori for d > 2. For each of these methods, we also present a scheme that gives the designer the flexibility of using different numbers of modes and wavelengths; the numbers of modes and wavelengths are two primary design parameters for the sawtooth slab waveguide. We also develop lower bounds on the cost of mapping tori on slab waveguides using a separable aggregate mapping. The mapping methods we propose in this thesis have different costs relative to the corresponding lower bounds. Some are optimal and match the lower bound, while for others, there is a gap between the upper and lower bounds. However, all the methods proposed show a marked improvement over a naive mapping. We also explore the possibility of using extra channels to reduce the overall cost in the setting of a hypercube topology.
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