We present a simple and natural greedy algorithm for the metric uncapacitated facility location problem achieving an approximation guarantee of 1.61 whereas the best previously known was 1.73. Furthermore, we will show that our algorithm has a property which allows us to apply the technique of Lagrangian relaxation. Using this property, we can nd better approximation algorithms for many variants of the facility location problem, such as the capacitated facility location problem with soft capacities and a common generalization of the k-median and facility location problem. We will also prove a lower bound on the approximability of the k-median problem.

We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861. The running time of our algorithm is O(m log m), where m is the total number of edges in the underlying complete bipartite graph between cities and facilities. We use our algorithm to improve recent results for some variants of the problem, such as the fault tolerant and outlier versions. In addition, we introduce a new variant which can be seen as a special case of the concave cost version of this problem.

We study two versions of the single sink buy-at-bulk network design problem. We are given a network and a single sink, and several sources which demand a certain amount of ow to be routed to the sink.

We give the first polylogarithmic-competitive online algorithms for two-metric network design problems. These problems are very general, including as special cases such problems as steiner tree, facility location, and concave-cost single commodity flow.

We consider a generalization of the classical facility location problem, where we require the solution to be fault-tolerant. Every demand point j is served by r j facilities instead of just one. The facilities other than the closest one are "backup" facilities for that demand, and will be used only if the closer facility (or the link to it) fails. Hence, for any demand, we assign non-increasing weights to the routing costs to farther facilities. The cost of assignment for demand j is the weighted linear combination of the assignment costs to its r j closest open facilities. We wish to minimize the sum of the cost of opening the facilities and the assignment cost of each demand j. We obtain a factor 4 approximation to this problem through the application of various rounding techniques to the linear relaxation of an integer program formulation. We further improve this...

We consider online problems where purchases have time durations which expire regardless of whether the purchase is used or not. The Parking Permit Problem is the natural analog of the well-studied skirental problem in this model, and we provide matching upper and lower bounds on the competitive ratio for this problem. 1

We present approximation algorithms for integrated logistics problems that combine elements of facility location and transport network design. We first study the problem where opening facilities incurs opening costs and transportation from the clients to the facilities incurs buy-at-bulk costs, and provide a combinatorial approximation algorithm. We also show that the integer programming formulation of this problem has small integrality gap. We extend the model to the version when there is a bound on the number of facilities that may be opened.

emerged as an interdisciplinary field that draws together chemistry,