A unified approach to approximation algorithms for bottleneck problems
Journal of the ACM (JACM)
Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
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
Asymmetric k-center is log* n-hard to approximate
Journal of the ACM (JACM)
Achieving anonymity via clustering
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A constant factor approximation algorithm for k-median clustering with outliers
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Streaming Algorithms for k-Center Clustering with Outliers and with Anonymity
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Non-monotone submodular maximization under matroid and knapsack constraints
Proceedings of the forty-first annual ACM symposium on Theory of computing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Budgeted red-blue median and its generalizations
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Approximation schemes for multi-budgeted independence systems
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Submodular function maximization via the multilinear relaxation and contention resolution schemes
Proceedings of the forty-third annual ACM symposium on Theory of computing
Constant factor approximation algorithm for the knapsack median problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Matroidal degree-bounded minimum spanning trees
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Efficient algorithms for the weighted k-center problem on a real line
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
A dependent LP-rounding approach for the k-median problem
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
The fault tolerant capacitated k-center problem
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
LP Rounding for k-Centers with Non-uniform Hard Capacities
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
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In the classic k-center problem, we are given a metric graph, and the objective is to open k nodes as centers such that the maximum distance from any vertex to its closest center is minimized. In this paper, we consider two important generalizations of k-center, the matroid center problem and the knapsack center problem. Both problems are motivated by recent content distribution network applications. Our contributions can be summarized as follows: 1 We consider the matroid center problem in which the centers are required to form an independent set of a given matroid. We show this problem is NP-hard even on a line. We present a 3-approximation algorithm for the problem on general metrics. We also consider the outlier version of the problem where a given number of vertices can be excluded as the outliers from the solution. We present a 7-approximation for the outlier version. 2 We consider the (multi-)knapsack center problem in which the centers are required to satisfy one (or more) knapsack constraint(s). It is known that the knapsack center problem with a single knapsack constraint admits a 3-approximation. However, when there are at least two knapsack constraints, we show this problem is not approximable at all. To complement the hardness result, we present a polynomial time algorithm that gives a 3-approximate solution such that one knapsack constraint is satisfied and the others may be violated by at most a factor of 1+ε. We also obtain a 3-approximation for the outlier version that may violate the knapsack constraint by 1+ε.