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In the stochastic knapsack problem, we are given a knapsack of size B, and a set of items whose sizes and rewards are drawn from a known probability distribution. To know the actual size and reward we have to schedule the item -- when it completes, we get to know these values. The goal is to schedule the items (possibly making adaptive decisions based on(More)
We consider the problem of computing efficient strategies for searching in trees. As a generalization of the classical binary search for ordered lists, suppose one wishes to find a (unknown) specific node of a tree by asking queries to its arcs, where each query indicates the endpoint closer to the desired node. Given the likelihood of each node being the(More)
In this paper we consider a relaxation of the corner polyhedron introduced by Andersen et al., which we denote by RCP. We study the relative strength of the split and triangle cuts of RCP's. Basu et al. showed examples where the split closure can be arbitrarily worse than the triangle closure under a 'worst-cost' type of measure. However, despite(More)
In this paper we report the development of two attachments to a commercial cell phone that transform the phone's integrated lens and image sensor into a 350x microscope and visible-light spectrometer. The microscope is capable of transmission and polarized microscopy modes and is shown to have 1.5 micron resolution and a usable field-of-view of 150 x 50(More)
A direct sum theorem for two parties and a function f states that the communication cost of solving k copies of f simultaneously with error probability 1/3 is at least k · R 1/3 (f), where R 1/3 (f) is the communication required to solve a single copy of f with error probability 1/3. We improve this for a natural family of functions f , showing that the(More)
We prove that any minimal valid function for the k-dimensional infinite group relaxation that is continuous piecewise linear with at most k + 1 slopes and does not factor through a linear map with non-trivial kernel is extreme. This generalizes a theorem of Gomory and Johnson for k = 1, and Cornuéjols and Molinaro for k = 2.
In this paper we consider the infinite relaxation of the corner poly-hedron with 2 rows. For the 1-row case, Gomory and Johnson proved in their seminal paper a sufficient condition for a minimal function to be extreme, the celebrated 2-Slope Theorem. Despite increased interest in understanding the multiple row setting, no generalization of this theorem was(More)
We consider packing LP's with m rows where all constraint coefficients are normalized to be in the unit interval. The n columns arrive in random order and the goal is to set the corresponding decision variables irrevocably when they arrive to obtain a feasible solution maximizing the expected reward. Previous (1 −)-competitive algorithms require the(More)
A function $$f(x_1, \ldots , x_d)$$ f ( x 1 , … , x d ) , where each input is an integer from 1 to $$n$$ n and output is a real number, is Lipschitz if changing one of the inputs by 1 changes the output by at most 1. In other words, Lipschitz functions are not very sensitive to small changes in the input. Our main result is an efficient tester for the(More)