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For bin packing, the input consists of n items with sizes s 1 ,. .. , s n ∈ [0, 1] which have to be assigned to a minimum number of bins of size 1. Recently, the second author gave an LP-based polynomial time algorithm that employed techniques from discrepancy theory to find a solution using at most OP T + O(logOP T · log logOP T) bins. In this paper, we… (More)

- Rebecca Hoberg, Giang Tran, Mckenzie West
- 2010

Let p(n) denote the ordinary partition function. In 1966, Subbarao [18] conjectured that in every arithmetic progression r (mod t) there are infinitely many integers N (resp. M) ≡ r (mod t) for which p(N) is even (resp. odd). We prove Subbarao's conjecture for all moduli t of the form m · 2 s where m ∈ {1, 5, 7, 17}. To obtain this theorem we make use of… (More)

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