Integer and combinatorial optimization
Integer and combinatorial optimization
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
The budgeted maximum coverage problem
Information Processing Letters
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Integrated Admission Control for Streaming and Elastic Traffic
COST 263 Proceedings of the Second International Workshop on Quality of Future Internet Services
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
Throughput-competitive on-line routing
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
A note on maximizing a submodular set function subject to a knapsack constraint
Operations Research Letters
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We consider the optimization problem of providing a set of video streams to a set of clients, where each stream has costs in m possible measures (such as communication bandwidth, processing bandwidth, etc.), and each client has its own utility function for each stream. We assume that the server has a budget cap on each of the m cost measures; each client has an upper bound on the utility that can be derived from it, and potentially also upper bounds in each of the m cost measures. The task is to choose which streams the server will provide, and out of this set, which streams each client will receive. The goal is to maximize the overall utility subject to the budget constraints. We give an efficient approximation algorithm with approximation factor of O(m) with respect to the optimal possible utility for any input, assuming that clients have only a bound on their maximal utility. If, in addition, each client has at most m"c capacity constraints, then the approximation factor increases by another factor of O(m"clogn), where n is the input length. We also consider the special case of ''small'' streams, namely where each stream has cost of at most O(1/logn) fraction of the budget cap, in each measure. For this case we present an algorithm whose approximation ratio is O(logn).