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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)

The perceptron algorithm for linear programming, arising from machine learning, has been around since the 1950s. While not a polynomial-time algorithm, it is useful in practice due to its simplicity and robustness. In 2004, Dunagan and Vempala showed that a randomized rescaling turns the per-ceptron method into a polynomial time algorithm, and later Peña… (More)

The number balancing (NBP) problem is the following: given real numbers a1,. .. , an ∈ [0, 1], find two disjoint subsets I1, I2 ⊆ [n] so that the difference | i∈I 1 ai − i∈I 2 ai| of their sums is minimized. An application of the pigeonhole principle shows that there is always a solution where the difference is at most O(√ n 2 n). Finding the minimum,… (More)

- REBECCA HOBERG
- 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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