Current Research

The current focus of my research is the investigation of structured information movement in distributed memory multiple processor systems, telephone switching systems, and LEO satellite networks. My main goal is to improve the performance of networks based on existing technologies by developing new information movement and switching algorithms, and new interconnection topologies. I do this by developing and using mathematical models that reflect the physical characteristics of networks as accurately as possible. Current and recently completed projects include:
  1. Comparisons of Switching Modes. I have been using linear cost models to study circuit-switched routing, store-and-forward routing, and variants such as line communication. New techniques include the use virtual channels to enhance performance, the use of tilings to solve broadcasting problems, and decompositions into parallel cycles to implement matrix operations such as transposition, reflection, and rotation which have applications in numerical computation, image processing, and computer vision.
  2. Lower Bounds in Communication Theory. I am currently working on a survey and classification of lower bound techniques with an emphasis on collective communication operations in direct networks. The vast majority of these lower bound techniques can be classified on the basis of a few parameters (e.g., General vs. Restricted Models, Synchronous vs. Asynchronous Communication) and a handful of proof techniques (e.g., Critical Paths, Flow-based Methods, Conflicting Time Paths). The goal of this work is to determine the limits and potentials of the proof techniques.
  3. Neighbourhood Communication. This type of communication problem occurs when one or more processors need to be aware of information stored by nearby processors. Recent work has concentrated on neighbourhood communication in hypercubes.

Editorial and Professional Activities: Program Committee Member - SIROCCO, 1999; Guest Editor - Discrete Applied Mathematics, 1998; Program Committee Member - 4th Workshop on Algorithms and Data Structures, 1995; Minitrack Coordinator, 28th Hawaii Int. Conf. on System Sciences, 1995; Co-chair - First Canada-France Conference on Parallel Computing, 1994;

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