Rebecca Hoberg

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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)
In this paper we examine two physically-inspired objects, knots and braids. The two are intimately related because when we connect the ends of a braid, we end up with a knot or link. We show that braids can be defined algebraically, geometrically, and topologically, and we determine when two braids will yield the same knot. Finally, we prove that every knot(More)
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