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Given data drawn from a mixture of multivariate Gaussians, a basic problem is to accurately estimate the mixture parameters. We give an algorithm for this problem that has running time and data requirements polynomial in the dimension and the inverse of the desired accuracy, with provably minimal assumptions on the Gaussians. As a simple consequence of our learning algorithm, we we give the first...
The notion of vertex sparsification (in particular cut-sparsification) is introduced in, where it was shown that for any graph G = (V, E) and any subset of k terminals K ⊂ V, there is a polynomial time algorithm to construct a graph H = (K, EH) on just the terminal set so that simultaneously for all cuts (A,K-A), the value of the minimum cut in G separating A from K-A is approximately the same as...
Linial, London and Rabinovich [16] and Aumann and Rabani [3] proved that the min-cut max-flow ratio for general maximum concurrent flow problems (when there are k commodities) is O(logfe). Here we attempt to derive a more general theory of Steiner cut and flow problems, and we prove bounds that are poly-logarithmic in k for a much broader class of multicommodity flow and cut problems. Our structural...
Geographic routing is a family of routing algorithms that uses geographic point locations as addresses for the purposes of routing. Such routing algorithms have proven to be both simple to implement and heuristically effective when applied to wireless sensor networks. Greedy routing is a natural abstraction of this model in which nodes are assigned virtual coordinates in a metric space, and these...
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