Using graph theory to reduce communication overhead in parallel systems

  • Authors:
  • David R. Surma

  • Affiliations:
  • Department of Computer and Information Sciences, Indiana University South Bend, South Bend, IN

  • Venue:
  • Journal of Computing Sciences in Colleges
  • Year:
  • 2003

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Abstract

Parallel computer systems are often used when dealing with problems requiring high amounts of computation. While it is apparent that having multiple processors can reduce the computation time, the amount of reduction is not directly proportional to the increased number of processors. Communication overhead diminishes these gains, and it is caused by the inherent message exchanges between individual processors. It was found that by scheduling these message exchanges better performance can be achieved. A model called a collision graph was developed to transform the scheduling problem into a graph problem. Solving the communication reduction problem is shown to be synonymous with determining a maximum independent set while also considering the graph colorability. Since these graph problems are NP-Complete, heuristics are used to determine communication schedules. This paper presents the graph model and discusses the graph theory that leads to the selection of heuristics used in the scheduling process. The complexity of the developed algorithms as well as their performance is presented and analyzed. Results show that by scheduling the communication improvement of over 35% can be obtained as compared to baseline techniques.