TY - JOUR

T1 - Reliable assignments of processors to tasks and factoring on matroids

AU - Colbourn, Charles J.

AU - Elmallah, Ehab S.

N1 - Funding Information:
Correspondence to: Charles J. Colbourn, Waterloo, Waterloo, Ont., Canada N2L 3Gl. * Research supported by NSERC Canada
Funding Information:
under grant number A0579 (CJC) and OGP36899

PY - 1993/4/28

Y1 - 1993/4/28

N2 - 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.

AB - 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.

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U2 - 10.1016/0012-365X(93)90360-6

DO - 10.1016/0012-365X(93)90360-6

M3 - Article

AN - SCOPUS:38249003677

VL - 114

SP - 115

EP - 129

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -