Theoretical Computer Science - Algorithmic applications in management
A constant factor approximation algorithm for k-median clustering with outliers
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Importance sampling via load-balanced facility location
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Improved approximation algorithms for the minimum latency problem via prize-collecting strolls
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A primal-dual approximation algorithm for the k-level stochastic facility location problem
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Approximation algorithms for 2-stage stochastic optimization problems
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Sampling bounds for stochastic optimization
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
An approximation algorithm for a facility location problem with inventories and stochastic demands
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
An approximation algorithm for the k-level stochastic facility location problem
Operations Research Letters
An approximation algorithm for a facility location problem with stochastic demands and inventories
Operations Research Letters
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In the metric uncapacitated facility location problem (UFLP), we are given a set of clients, a set of facilities, an opening cost for each facility, and a connection cost between each client and each facility satisfying the metric inequality. The objective is to open a subset of facilities and connect each client to an open facility so that the total cost of opening facilities and connecting clients to facilities is minimized. As the UFLP is NP-hard, much effort has been devoted to designing approximation algorithms for it. As our main result, we introduce a method called dual fitting and use it in conjunction with factor-revealing programs to obtain improved approximation algorithms for the UFLP. Our best algorithm achieves an approximation factor of 1.52 (currently the best known factor) and runs in quasilinear time. We demonstrate the versatility of our techniques by using them to analyze the approximation factors of a cycle cover algorithm and a Steiner packing algorithm, as well as the competitive factor of an online buffer management algorithm. We also use our algorithms and other techniques to improve the approximation factors of several variants of the UFLP. In particular, we introduce the notion of bifactor approximate reductions and use it to derive a 2-approximation for the soft-capacitated FLP. Finally, we consider the UFLP in a game-theoretic setting and prove tight bounds on schemes for dividing up the cost of a solution among players. Our result combined with the scheme proposed by Pál and Tardos shows that 1/3 is the best possible approximation factor of any cross-monotonic cost-sharing scheme for the UFLP. Our proof uses a novel technique that we apply to several other optimization problems. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)