CS 789 THEORY SEMINAR [home]

Speaker:  Ranjithkumar Rajagopalan
Affiliation: ORIE, Cornell University
Date: Monday, September 8, 2003
Title: Langranian relaxation for the k-median problem:  new insights and continuity properties

Abstract:

This work gives new insight into two well-known approximation algorithms for the uncapacitated facility location problem: the primal-dual algorithm of Jain & Vazirani, and an algorithm of Mettu & Plaxton. Our main result answers positively a question posed by Jain & Vazirani of whether their algorithm can be modified to attain a desired "continuity" property. This yields an upper bound of 3 on the integrality gap of the natural LP relaxation of the k-median problem, but our approach does not yield a polynomial time algorithm with this guarantee. We also give a new simple proof of the performance guarantee of the Mettu-Plaxton algorithm using LP duality, which suggests a minor modification of the algorithm that makes it Lagrangian-multiplier preserving.