Reliable assignments of processors to tasks and factoring on matroids

Charles J. Colbourn, Ehab S. Elmallah

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In the simple assignment problem, there are n processors, m tasks, and a relation between the processors and tasks; this relation indicates the ability of the processor to perform the task. When the processors fail independently with known probabilities, two performance issues arise. First, with what probability can the operating processors all be kept busy? Second, with what probability can the operating processors perform the same number of tasks that all processors could? We formulate these questions on the underlying transversal matroid. We first prove that counting minimum cardinality circuits in this matroid is # P-complete and, hence, that both questions are also # P-complete. Secondly, we devise a factoring algorithm with series and parallel reductions to compute the exact solutions of the above problems. We then outline some efficient strategies for bounding the probabilities.

Original languageEnglish (US)
Pages (from-to)115-129
Number of pages15
JournalDiscrete Mathematics
Volume114
Issue number1-3
DOIs
StatePublished - Apr 28 1993

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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