Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
A multiplier adjustment method for the generalized assignment problem
Management Science
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
e-approximations with minimum packing constraint violation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Greedy strikes back: improved facility location algorithms
Journal of Algorithms
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Analysis of a local search heuristic for facility location problems
Journal of 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
A new greedy approach for facility location problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Algorithms for Capacitated Facility Location Problems
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximation algorithms for facility location problems
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Improved Approximation Algorithms for Metric Facility Location Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
A Greedy Facility Location Algorithm Analyzed Using Dual Fitting
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Facility Location with Nonuniform Hard Capacities
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Improved Approximation Algorithms for the Uncapacitated Facility Location Problem
SIAM Journal on Computing
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Improved approximation algorithms for capacitated facility location problems
Mathematical Programming: Series A and B
Tight approximation algorithms for maximum general assignment problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Proceedings of the 17th international conference on World Wide Web
An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
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
Assignment problem in content distribution networks: unsplittable hard-capacitated facility location
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Design and deployment of a digital forensics service platform for online videos
MiFor '09 Proceedings of the First ACM workshop on Multimedia in forensics
Proactive data dissemination to mission sites
SECON'09 Proceedings of the 6th Annual IEEE communications society conference on Sensor, Mesh and Ad Hoc Communications and Networks
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In a Content Distribution Network (CDN), there are m servers storing the data; each of them has a specific bandwidth. All the requests from a particular client should be assigned to one server because of the routing protocol used. The goal is to minimize the total cost of these assignments—cost of each is proportional to the distance between the client and the server as well as the request size—while the load on each server is kept below its bandwidth limit. When each server also has a setup cost, this is an unsplittable hard-capacitated facility location problem. As much attention as facility location problems have received, there has been no nontrivial approximation algorithm when we have hard capacities (i.e., there can only be one copy of each facility whose capacity cannot be violated) and demands are unsplittable (i.e., all the demand from a client has to be assigned to a single facility). We observe it is NP-hard to approximate the cost to within any bounded factor in this case. Thus, for an arbitrary constant ε0, we relax the capacities to a 1+ε factor. For the case where capacities are almost uniform, we give a bicriteria O(log n, 1+ε)-approximation algorithm for general metrics and a (1+ε, 1+ε)-approximation algorithm for tree metrics. A bicriteria (α,β)-approximation algorithm produces a solution of cost at most α times the optimum, while violating the capacities by no more than a β factor. We can get the same guarantees for nonuniform capacities if we allow quasipolynomial running time. In our algorithm, some clients guess the facility they are assigned to, and facilities decide the size of the clients they serve. A straightforward approach results in exponential running time. When costs do not satisfy metricity, we show that a 1.5 violation of capacities is necessary to obtain any approximation. It is worth noting that our results generalize bin packing (zero connection costs and facility costs equal to one), knapsack (single facility with all costs being zero), minimum makespan scheduling for related machines (all connection costs being zero), and some facility location problems.