Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
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We investigate an extension of the randomized rounding technique introduced by Raghavan and Thompson. Whereas their approach only requires that each variable is rounded with probabilities given by its fractional part, we also impose this condition on several sums of variables. Thus in particular our roundings are not independent.We show that such non-independent randomized roundings exist if and only if the hypergraph corresponding to these dependencies is totally unimodular.