Abstract
If the set covering constraints are Ax ⩾ 1 and x j ∈ {0,1}, the prior probability that the jth subset participates in an optimal covering (independently of subset costs) is shown to be given by the principal row eigenvector of A ∗A , where a ji ∗ = 1 − a ij . These probabilities lead to new and interesting objective functions, which are shown to be equivalent to cross entropy or weighted cross-entropy. The probabilities can also be used to obtain better bounds for heuristic solutions to optimal covering and set representation problems.
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