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The analysis of matrices associated with discrete, pairwise comparisons can be a very useful toolbox for a computer scientist. In particular, Spectral Graph Theory is based on the observation that eigenvalues and eigenvectors of these matrices betray a lot of properties of graphs associated with them. The first major section of this paper is a survey of key(More)
Suppose that we sequentially place n balls into n boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability (1 + o(1)) ln n/ ln ln n balls in it. Suppose instead that for each ball we choose two boxes at random and place the ball into the one which is less full at the time of(More)
This paper studies the depth of noisy decision trees in which each node gives the wrong answer with some constant probability. In the noisy Boolean decision tree model, tight bounds are given on the number of queries to input variables required to compute threshold functions, the parity function and symmetric functions. In the noisy comparison tree model,(More)
We analyze the pure literal rule heuristic for computing a satisfying assignment to a random 3-CNF formula with n variables. We show that the pure literal rule by itself finds satisfying assignments for almost all 3-CNF formulas with up to 1.63n clauses, but it fails for more than 1.7n clauses. As an aside we show that the value of maximum satis-fiability(More)
We present efficient algorithms for two all-to-all communication operations in message-passing systems: <italic>index</italic> (or all-to-all personalized communication) and <italic>concatenation</italic> (or all-to-all broadcast). We assume a model of a fully-connected message-passing system, in which the performance of any point-to-point communication is(More)
Next-generation DNA sequencing technologies are enabling genome-wide measurements of somatic mutations in large numbers of cancer patients. A major challenge in the interpretation of these data is to distinguish functional "driver mutations" important for cancer development from random "passenger mutations." A common approach for identifying driver(More)
Recent work on modeling the Web graph has dwelt on capturing the degree distributions observed on the Web. Pointing out that this represents a heavy reliance on " local " properties of the Web graph, we study the distribution of PageRank values (used in the Google search engine) on the Web. This distribution is of independent interest in optimizing search(More)
Communication in all-optical networks requires novel routing paradigms. The high bandwidth of the optic fiber is utilized through wavelength-division multiplexing: a single physical optical link can carry several logical signals, provided that they are transmitted on different wavelengths. We study the problem of routing a set of requests (each of which is(More)