STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Competitive non-preemptive call control
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Combining online algorithms for rejection and acceptance
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A general approach to online network optimization problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Improved combination of online algorithms for acceptance and rejection
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Journal of Scheduling - Special issue: On-line algorithm part I
Approximating the online set multicover problems via randomized winnowing
Theoretical Computer Science
The Design of Competitive Online Algorithms via a Primal: Dual Approach
Foundations and Trends® in Theoretical Computer Science
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We study the admission control problem in general networks.Communication requests arrive over time, and the online algorithmaccepts or rejects each request while maintaining the capacitylimitations of the network. The admission control problem has beenusually analyzed as a benefit problem, where the goal is to devisean online algorithm that accepts the maximum number of requestspossible. The problem with this objective function is that evenalgorithms with optimal competitive ratios may reject almost all ofthe requests, when it would have been possible to reject only afew. This could be inappropriate for settings in which rejectionsare intended to be rare events.In this paper, we consider preemptive online algorithms whosegoal is to minimize the number of rejected requests. Each requestarrives together with the path it should be routed on. We show anO(log2(mc))-competitiverandomized algorithm for the weighted case, wherem is the number of edges in the graph andc is the maximum edge capacity. For theunweighted case, we give an O(logm log c)-competitiverandomized algorithm. This settles an open question of Blum, Kalaiand Kleinberg raised in [10]. We note that allowing preemption andhandling requests with given paths are essential for avoidingtrivial lower bounds.The admission control problem is a generalization of the onlineset cover with repetitions problem, whose input is a family ofm subsets of a ground set ofn elements. Elements of the ground set are givento the online algorithm one by one, possibly requesting eachelement a multiple number of times. (If each element arrives atmost once, this corresponds to the online set cover problem.) Thealgorithm must cover each element by different subsets, accordingto the number of times it has been requested.We give an O(log m logn)-competitive randomized algorithm for theonline set cover with repetitions problem. This matches a recentlower bound of Ω(log m logn) given by Feige and Korman for the competitiveratio of any randomized polynomial timealgorithm, under the BPP ≠NP assumption. Given any constant ε 0, an O(log mlogn)-competitive deterministic bicriteriaalgorithm is shown that covers each element by at least(1-ε)k sets, where kis the number of times the element is covered by the optimalsolution.