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1 Overview In this lecture we will talk about adaptive sparse recovery. 2 Adaptivity in group testing In sparse recovery, we have y = Ax = In our previous non-adaptive setting, v i 's were chosen independently. Intuitively, it seems we may be able to do better if they are not independent. So, in the adaptive setting we talk about today, The idea is, for(More)
1 Overview In this lecture we will talk about information and compression, which the Huffman coding can achieve with the average number of bits sent almost precisely equal to the entropy. Then we will talk about communication complexity and information cost, which is the asymptotic number of bits two parties need to transmit in a conversation in order to(More)
We present improved algorithms to match two polygonal shapes P and Q to approximate their maximum overlap. Let n be their total number of vertices. Our first algorithm finds a translation that approximately maximizes the overlap area of P and Q under translation in O(n 2 ε −3) time. The error is additive and it is at most ε · min{area(P), area(Q)} with(More)
We study variants of the stable marriage and college admissions models in which the agents are allowed to express weak preferences over the set of agents on the other side of the market and the option of remaining unmatched. For the problems that we address, previous authors have presented polynomial-time algorithms for computing a " Pareto-stable "(More)
<lb>We study the variant of the stable marriage problem in which the preferences of the agents<lb>are allowed to include indifferences. We present a mechanism for producing Pareto-stable<lb>matchings in stable marriage markets with indifferences that is group strategyproof for one<lb>side of the market. Our key technique involves modeling the stable(More)
Consider a complete weighted bipartite graph G in which each left vertex u has two real numbers intercept and slope, each right vertex v has a real number quality, and the weight of any edge (u, v) is defined as the intercept of u plus the slope of u times the quality of v. Let m (resp., n) denote the number of left (resp., right) vertices, and assume that(More)
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