A unified approach to approximation algorithms for bottleneck problems
Journal of the ACM (JACM)
A heuristic for the p-center problem in graphs
Discrete Applied Mathematics
The p-neighbor k-center problem
Information Processing Letters
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
Fault tolerant K-center problems
Theoretical Computer Science
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Local search heuristic for k-median and facility location problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Facility Location with Dynamic Distance Function (Extended Abstract)
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
Improved Approximation Algorithms for Metric Facility Location Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Asymmetric k-center is log* n-hard to approximate
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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This paper explores three concepts: the k-center problem, some of its variants, and asymmetry. The k-center problem is fundamental in location theory. Variants of k-center may more accurately model real-life problems than the original formulation. Asymmetry is a significant impediment to approximation in many graph problems, such as k-center, facility location, k-median, and the TSP.We give an O(log*n)-approximation algorithm for the asymmetric weighted k-center problem. Here, the vertices have weights and we are given a total budget for opening centers. In the p-neighbor variant each vertex must have p (unweighted) centers nearby: we give an O(log*k)-bicriteria algorithm using 2k centers, for small p.Finally, we show the following three versions of the asymmetric k-center problem to be inapproximable: priority k-center, k-supplier, and outliers with forbidden centers.