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The information complexity of a function f is the minimum amount of information Alice and Bob need to exchange to compute the function f. In this paper we provide an algorithm for approximating the information complexity of an arbitrary function f to within any additive error α > 0, thus resolving an open question as to whether information complexity is(More)
Motivated by applications in recommender systems, web search, social choice and crowdsourcing, we consider the problem of identifying the set of top K items from noisy pairwise comparisons. In our setting, we are non-actively given r pairwise comparisons between each pair of n items, where each comparison has noise constrained by a very general noise model(More)
We consider the manipulability of tournament rules for round-robin tournaments of n competitors. Specifically , n competitors are competing for a prize, and a tournament rule r maps the result of all n 2 pairwise matches (called a tournament, T) to a distribution over winners. Rule r is Condorcet-consistent if whenever i wins all n − 1 of her matches, r(More)
In this note we obtain tight bounds on the space-complexity of computing the ergodic measure of a low-dimensional discrete-time dynamical system affected by Gaussian noise. If the scale of the noise is ε, and the function describing the evolution of the system is not by itself a source of computational complexity, then the density function of the ergodic(More)
In this paper, we study the problem of fast dynamic pointer following: given a directed graph G where each vertex has outdegree 1, efficiently support the operations of i) changing the outgoing edge of any vertex, and ii) find the vertex k vertices 'after' a given vertex. We exhibit a solution to this problem based on link-cut trees that requires O(lg n)(More)
In the previous lecture, we began our discussion of pseudorandomness. We presented the Blum-Micali definition of a pseudorandom generator, which defines pseudorandomness in terms of how hard it is for members of a specific computation class to distinguish between true randomness and generated randomness. We proved Yao's theorem, which provides a link(More)
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