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Approximation Algorithms for Geometric Median Problems (1992) [59 citations — 0 self]

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@MISC{Lin92approximationalgorithms,
    author = {Jyh-Han Lin and Jeffrey Scott Vitter},
    title = {Approximation Algorithms for Geometric Median Problems},
    year = {1992}
}

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Abstract:

In this paper we present approximation algorithms for median problems in metric spaces and fixed-dimensional Euclidean space. Our algorithms use a new method for transforming an optimal solution of the linear program relaxation of the s-median problem into a provably good integral solution. This transformation technique is fundamentally different from the methods of randomized and deterministic rounding [Rag, RaT] and the methods proposed in [LiV] in the following way: Previous techniques never set variables with zero values in the fractional solution to 1. This departure from previous methods is crucial for the success of our algorithms.

Citations

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243	Probabilistic construction of deterministic algorithms: approximating packing integer programs – Raghavan - 1988
238	Randomized Rounding: A Technique for Provably Good Algorithms and Algorithmic – Raghavan, Thompson - 1987
170	Clustering to minimize the maximum intercluster distance – Gonzalez - 1985
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55	ǫ-Approximations with Minimum Packing Constraint Violation – Lin, Vitter
45	ffl-Approximations with minimum packing constraint – Lin, Vitter - 1992