Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems
نویسندگان
چکیده
We present approximation algorithms for the metric uncapacitated facility location problem and the metric k-median problem achieving guarantees of 3 and 6 respectively. The distinguishing feature of our algorithms is their low running time: O(m log m) and O(m logm(L+log(n))) respectively, where n and m are the total number of vertices and edges in the underlying graph. The main algorithmic idea is a new extension of the primal-dual schema to handle a primal-dual pair of LP's that are not a covering-packing pair.
منابع مشابه
Approximate k-MSTs and k-Steiner Trees via the Primal-Dual Method and Lagrangean Relaxation
Garg [10] gives two approximation algorithms for the minimum-cost tree spanning k vertices in an undirected graph. Recently Jain and Vazirani [15] discovered primal-dual approximation algorithms for the metric uncapacitated facility location and k-median problems. In this paper we show how Garg’s algorithms can be explained simply with ideas introduced by Jain and Vazirani, in particular via a ...
متن کاملA Systematic Approach to Bound Factor Revealing LPs and Its Application to the Metric and Squared Metric Facility Location Problems
A systematic technique to bound factor-revealing linear programs is presented. We show how to derive a family of upper bound factor-revealing programs (UPFRP), and that each such program can be solved by a computer to bound the approximation factor. Obtaining an UPFRP is straightforward, and can be used as an alternative to analytical proofs, that are usually very long and tedious. We apply thi...
متن کاملImproved Combinatorial Algorithms for the Facility Location and k-Median Problems
We present improved combinatorial approximation algorithms for the uncapacitated facility location and k-median problems. Two central ideas in most of our results are cost scaling and greedy improvement. We present a simple greedy local search algorithm which achieves an approximation ratio of 2:414+ in ~ O(n= ) time. This also yields a bicriteria approximation tradeo of (1+ ; 1+ 2= ) for facil...
متن کاملAlgorithms with Provable Guarantees for Clustering
In this talk, we give an overview of the current best approximation algorithms for fundamental clustering problems, such as k-center, k-median, k-means, and facility location. We focus on recent progress and point out several important open problems. For the uncapacitated versions, a variety of algorithmic methodologies, such as LP-rounding and primal-dual method, have been applied to a standar...
متن کاملCombinatorial Interpretations of Dual Fitting and Primal Fitting
We present two new combinatorial approximation frameworks that are not based on LPduality, or even on linear programming. Instead, they are based on weight manipulation in the spirit of the local ratio technique. We show that the first framework is equivalent to the LP based method of dual fitting and that the second framework is equivalent to an LP-based method which we define and call primal ...
متن کامل