Combinatorics, Probability and Computing
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Motivated by a scheduling problem that arises in the study of optical networks, we prove the following result, which is a variation of a conjecture of Haxell, Wilfong and Winkler.Let $k,n$ be two positive integers, let $w_{sj}, 1 \leq s \leq n, 1 \leq j \leq k$ be nonnegative reals satisfying $\sum_{j=1}^k w_{sj}