Lecture 5: Primal-Dual Algorithms and Facility Location

Cs880: Approximations Algorithms

Last time we discussed how LP-duality can be applied to approximation. We introduced the primaldual method for approximating the optimal solution to an LP in a combinatorial way. We applied this technique to give another 2-approximation for the Vertex Cover problem. In this lecture, we present and analyze a primal-dual algorithm that gives a 2-approximation for the Steiner Forest problem. We al...

CS G 399 : Algorithmic Power Tools I Scribe : Bishal Thapa

In this lecture, we first complete the analysis of “Greedy” approach we introduced in the last lecture, that gives a constant (6)-approximation polynomial-time solution for the Uncapacitated Facility Location problem. Then, we present a primal-dual approach of solving the problem, that yields a better approximation solution of cost within a factor of 3 of the optimal. The latter has a polynomia...

Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems

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...

Primal-Dual Algorithms for Connected Facility Location Problems

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 ...