Combining online algorithms for rejection and acceptance

Azar, Yossi; Blum, Avrim; Mansour, Yishay

doi:10.1145/777412.777438

Cited by 7 publications

(4 citation statements)

References 9 publications

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“…There has been a huge literature [11,12,13,14,15] on Routing in Networks and Load Balancing where preemption of previously allocated resources in allowed. Many of these results studied can be very succinctly generalized by the following problem.…”

Section: Routing With Preemption and Load Balancingmentioning

confidence: 99%

“…This could be by allowing the input to be either a random permutation [1,2,3,4,5] or drawn iid from some probability distribution [6,7]. Other approach [8,9,10,11,12,13,14,15] which does not relax any conditions on the input assumes that either preemption is allowed or preemption with a penalty is allowed and gives guarantee for every input. In this paper we study this kind of relaxation.…”

Section: Introductionmentioning

confidence: 99%

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Buyback Problem - Approximate matroid intersection with cancellation costs

Ashwinkumar

2010

Preprint

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In the buyback problem, an algorithm observes a sequence of bids and must decide whether to accept each bid at the moment it arrives, subject to some constraints on the set of accepted bids. Decisions to reject bids are irrevocable, whereas decisions to accept bids may be canceled at a cost that is a fixed fraction of the bid value. Previous to our work, deterministic and randomized algorithms were known when the constraint is a matroid constraint. We extend this and give a deterministic algorithm for the case when the constraint is an intersection of k matroid constraints. We further prove a matching lower bound on the competitive ratio for this problem and extend our results to arbitrary downward closed set systems. This problem has applications to banner advertisement, semi-streaming, routing, load balancing and other problems where preemption or cancellation of previous allocations is allowed.

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Section: Routing With Preemption and Load Balancingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Buyback Problem - Approximate matroid intersection with cancellation costs

Ashwinkumar

2010

Preprint

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“…They raised the question of whether an online algorithm with polylogarithmic competitive ratio can be obtained. We note that one can combine an algorithm for maximizing throughput of accepted requests and an algorithm for minimizing rejections and get one algorithm which achieves both simultaneously with slightly degrading the competitive ratio [9,11].…”

Section: Introductionmentioning

confidence: 99%

Admission control to minimize rejections and online set cover with repetitions

Alon

Azar

Gutner

2009

ACM Trans. Algorithms

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We study the admission control problem in general networks. Communication requests arrive over time, and the online algorithm accepts or rejects each request while maintaining the capacity limitations of the network. The admission control problem has been usually analyzed as a benefit problem, where the goal is to devise an online algorithm that accepts the maximum number of requests possible. The problem with this objective function is that even algorithms with optimal competitive ratios may reject almost all of the requests, when it would have been possible to reject only a few. This could be inappropriate for settings in which rejections are intended to be rare events.In this paper, we consider preemptive online algorithms whose goal is to minimize the number of rejected requests. Each request arrives together with the path it should be routed on. We show an O(log 2 (mc))-competitive randomized algorithm for the weighted case, where m is the number of edges in the graph and c is the maximum edge capacity. For the unweighted case, we give an O(log m log c)-competitive randomized algorithm. This settles an open question of Blum, Kalai and Kleinberg raised in [10]. We note that allowing preemption and handling requests with given paths are essential for avoiding trivial lower bounds.The admission control problem is a generalization of the online set cover with repetitions problem, whose input is a family of m subsets of a ground set of n elements. Elements * Research supported in part by a grant from the Israel Science Foundation, and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. of the ground set are given to the online algorithm one by one, possibly requesting each element a multiple number of times. (If each element arrives at most once, this corresponds to the online set cover problem.) The algorithm must cover each element by different subsets, according to the number of times it has been requested.We give an O(log m log n)-competitive randomized algorithm for the online set cover with repetitions problem. This matches a recent lower bound of Ω(log m log n) given by Feige and Korman for the competitive ratio of any randomized polynomial time algorithm, under the BP P = N P assumption. Given any constant > 0, an O(log m log n)-competitive deterministic bicriteria algorithm is shown that covers each element by at least (1 − )k sets, where k is the number of times the element is covered by the optimal solution.

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“…However, if OP T accepts 50% of the input, algorithm A accepts at least 25%, but algorithm R may accept nothing. Azar, Blum, and Mansour [1] cite examples of each type of algorithm and give an algorithm SW IT CH to combine a c Aaccept-competitive algorithm A and a c R -reject-competitive algorithm R into an algorithm that is simultaneously O(c 2 A )-accept-competitive and O(c A c R )-reject-competitive. The main idea behind SW IT CH is to alternately run algorithms A and R depending on the proportion of calls accepted by an offline optimal solution for σ t , the input up to time t. It requires explictly knowing the values of c A and c R .…”

Section: Introductionmentioning

confidence: 99%

Improved combination of online algorithms for acceptance and rejection

Bunde

Mansour

2004

Proceedings of the Sixteenth Annual ACM Symposium on Parallelism in Algorithms and Architectures

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Given two admission control algorithms that are c A -acceptcompetitive and c R -reject-competitive respectively, we give two ways to make an algorithm that is simultaneously O(c A )-accept-competitive and O(c A c R )-reject-competitive. The combined algorithms make no reference to the offline optimal solution. In addition, one of the algorithms does not require knowing the value of either c A or c R . This improves on work of Azar, Blum, and Mansour, whose combined algorithm was O(c 2 A )-accept-competitive, involved computing offline optimal solutions, and required knowing the values of both c A and c R .

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Combining online algorithms for rejection and acceptance

Cited by 7 publications

References 9 publications

Buyback Problem - Approximate matroid intersection with cancellation costs

Buyback Problem - Approximate matroid intersection with cancellation costs

Admission control to minimize rejections and online set cover with repetitions

Improved combination of online algorithms for acceptance and rejection

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