Distributing resources in hypercube computers

  • Authors:

  • M. Livingston;Q. F. Stout

  • Affiliations:

  • Department of Computer Science, Southern Illinois University, Edwardsville, IL;Dept. of Elect. Eng. and Comp. Sci., University of Michigan, Ann Arbor, MI

  • Venue:
  • C3P Proceedings of the third conference on Hypercube concurrent computers and applications: Architecture, software, computer systems, and general issues - Volume 1
  • Year:
  • 1988

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Abstract

Given a type of resource such as disk units, extra memory modules, connections to the host processor, or software modules, we consider the problem of distributing the resource units to processors in a hypercube computer so that certain performance requirements are met at minimal cost. Typical requirements include the condition that every processor is within a given distance of a resource unit, that every processor is within a given distance of each of several resources, and that every m-dimensional subcube contains a resource unit. The latter is particularly important in a multiuser system in which different users are given their own subcubes. In this setting, we also consider the problem of meeting the performance requirements at minimal cost when the subcube allocation system cannot allocate all possible subcubes and the requirements apply only to allocable subcubes. We also analyze the problem of partitioning processors with resources into different classes, requiring that every processor is within a given distance of, or in a subcube of given dimension with, a member of each class. Efficient constructive techniques for distributing or partitioning a resource are given for several performance requirements, along with upper and lower bounds on the total number of resource units required.