Isomorphic Routing on a Toroidal Mesh

Abstract

We study a routing problem that arises on SIMD parallel architectures whose communication network forms a toroidal mesh. We assume there exists a set of k message descriptors (xi, yi) , where (xi, yi) indicates that the ith message's recipient is offset from its sender by xi hops in one mesh dimension, and yi hops in the other. Every processor has k messages to send, and all processors use the same set of message routing descriptors. The SIMD constraint implies that at any routing step, every processor is actively routing messages with the same descriptors as any other processor. We call this Isomorphic Routing. Our objective is to find the isomorphic routing schedule with least makespan. We consider a number of variations on the problem, yielding complexity results from O(k) to NP-complete. Most of our results follow after we transform the problem into a scheduling problem, where it is related to other well-known scheduling problems.... Message routing, Network, Scheduling, Complexity, Algorithms.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1993
Accession Number
ADA263152

Entities

People

  • David M. Nicol
  • Weizhen Mao

Tags

Communities of Interest

  • Human Systems
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Communication Channels
  • Communication Networks
  • Computations
  • Computer Networks
  • Computer Science
  • Computers
  • Continuity
  • Contracts
  • Coordinate Systems
  • Engineering
  • Gantt Charts
  • Parallel Computing
  • Production Engineering
  • Scheduling (Production)
  • Switches
  • Workload

Fields of Study

  • Computer science

Readers

  • Approximation Theory.
  • Computer Networking
  • Operations Research