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• W169553655 abstract "In this paper, we revisit the classical k-median problem. Using the standard LP relaxation for k-median, we give an efficient algorithm to construct a probability distribution on sets of k centers that matches the marginals specified by the optimal LP solution. Analyzing the approximation ratio of our algorithm presents significant technical difficulties: we are able to show an upper bound of 3.25. While this is worse than the current best known 3 + ε guarantee of [2], because: (1) it leads to 3.25 approximation algorithms for some generalizations of the k-median problem, including the k-facility location problem introduced in [10], (2) our algorithm runs in (tilde{O}(k^3 n^2/delta^2)) time to achieve 3.25(1 + δ)-approximation compared to the O(n 8) time required by the local search algorithm of [2] to guarantee a 3.25 approximation, and (3) our approach has the potential to beat the decade old bound of 3 + ε for k-median.We also give a 34-approximation for the knapsack median problem, which greatly improves the approximation constant in [13]. Using the same technique, we also give a 9-approximation for matroid median problem introduced in [11], improving on their 16-approximation." @default.
• W169553655 created "2016-06-24" @default.
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• W169553655 date "2012-01-01" @default.
• W169553655 modified "2023-10-15" @default.
• W169553655 title "A Dependent LP-Rounding Approach for the k-Median Problem" @default.
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• W169553655 doi "https://doi.org/10.1007/978-3-642-31594-7_17" @default.
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