e-approximations with minimum packing constraint violation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A constant-factor approximation algorithm for the k-median problem (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Building Steiner trees with incomplete global knowledge
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Hierarchical placement and network design problems
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
A profit-maximizing supply chain network design model with demand choice flexibility
Operations Research Letters
Concurrency and Computation: Practice & Experience
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We consider opening facilities in order to gain a profit. We are given a set of demand points, and we must open some set of facilities such that every demand may be satisfied from a local facility and the total profit gained in this process is maximized. This contrasts with previous work on facility location and k-center problems, where opening a facility incurred a cost. The profit gained by opening a facility is a function of the amount of demand the facility satisfies. We model the dependence of profit on demand by creating many different possible facilities at each location, each of which provides a certain profit if opened and requires at least a certain amount of demand in order to open. Our model captures problem instances where profits may be positive or negative, and also instances where it is not necessary to satisfy every demand. Our algorithms provide the optimum total profit, while stretching the definition of locality by a constant and violating the required demands by a constant. We prove that without this stretch, the problem becomes NP-Hard to approximate.