A unified approach to approximation algorithms for bottleneck problems
Journal of the ACM (JACM)
e-approximations with minimum packing constraint violation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An O(log*n) approximation algorithm for the asymmetric p-center problem
Journal of Algorithms
An O(log*n) approximation algorithm for the asymmetric p-center problem
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Small Approximate Pareto Sets for Bi-objective Shortest Paths and Other Problems
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Resource minimization for fire containment
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
SIAM Journal on Computing
Optimal lower bounds for universal and differentially private steiner trees and TSPs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Discrete sensor placement problems in distribution networks
Mathematical and Computer Modelling: An International Journal
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Given a set V of n points and the distances between each pair, the k-center problem asks us to choose a subset C ⊆ V of size k that minimizes the maximum over all points of the distance from C to the point. This problem is NP-hardev en when the distances are symmetric and satisfy the triangle inequality, and Hochbaum and Shmoys gave a best-possible 2-approximation for this case. We consider the version where the distances are asymmetric. Panigrahy and Vish wanathan gave an O(log* n)-approximation for this case, leading many to believe that a constant approximation factor shouldb e possible. Their approach is purely combinatorial. We show how to use a natural linear programming relaxation to define a promising new measure of progress, anduse it to obtain two different O(log*k)-approximation algorithms. There is hope of obtaining further improvement from this LP, since we do not know of an instance where it has an integrality gap worse than 3.