Abstract
AbstractGiven a system of linear equations in an ‐vector of 0–1 variables, we compute the expectation of , where is a vector of independent Bernoulli random variables and are constants. The algorithm runs in quasi‐polynomial time under some sparseness condition on the matrix of the system. The result is based on the absence of the zeros of the analytic continuation of the expectation for complex probabilities, which can also be interpreted as the absence of a phase transition in the Ising model with a sufficiently strong external field. We discuss applications to perfect matchings in hypergraphs and randomized rounding in discrete optimization.
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