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Improved Approximation Algorithms for the Partial Vertex Cover Problem
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Approximation algorithms for partial covering problems
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Tight approximation algorithms for maximum general assignment problems
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Quorum placement in networks: minimizing network congestion
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Stream sampling for variance-optimal estimation of subset sums
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Efficient Stream Sampling for Variance-Optimal Estimation of Subset Sums
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Generating randomized roundings with cardinality constraints and derandomizations
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Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
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Improved approximation algorithms for the Min-Max Selecting Items problem
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We consider a family of distributions on fixed-weight vectors in (0; 1)t these distributions enjoy certain negative correlation properties and also satisfy pre-specified conditions on their marginal distributions. We show the existence of such families, and present a linear-time algorithm to sample from them. This yields improved approximation algorithms for the following problems: (a) low-congestion multi-path routing; (b) maximum coverage versions of set cover; (c) partial vertex cover problems for bounded-degree graphs; and (d) the Group Steiner Tree problem. For (a) and (b), the improvement is in the approximation ratio; for (c), we show how to speedup existing approximation algorithms while preserving the best-known approximation ratio; we also improve the approximation ratio for certain families of instances of unbounded degree. For (d), we derive an approximation algorithm whose approximation guarantee is at least as good as what is known; our algorithm is shown to have a better approximation guarantee for the worst known input families for existing algorithms.