Isomorphic routing on a toroidal mesh

Weizhen Mao, David M. Nicol

Research output: Contribution to journalArticlepeer-review


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 {(xp, yi)|i = 1, 2, . . ., k}, where (xp, 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 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 the minimum 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.

Original languageEnglish (US)
Pages (from-to)63-71
Number of pages9
JournalINFORMS Journal on Computing
Issue number1
StatePublished - 1996
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Computer Science Applications
  • Management Science and Operations Research

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