Oblivious Algorithms for the Maximum Directed Cut Problem

Feige, Uriel; Jozeph, Shlomo

doi:10.1007/s00453-013-9806-z

Cited by 16 publications

(9 citation statements)

References 25 publications

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“…Compared to the related result in [24], we remark that our analysis is substantially different due to the use of linear programming. This technique for the analysis of purely combinatorial algorithms has found applications in many different contexts such as facility location [22], set cover [7], online matching [30], maximum directed cut [16], wavelength routing [11], and revenue optimization [2]. Like in our case, these techniques usually lead to tight analysis.…”

Section: Related Workmentioning

confidence: 99%

Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship

Caragiannis

Filos-Ratsikas

Frederiksen

et al. 2016

Web and Internet Economics

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We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space are assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the social cost, i.e., the total distance between the most-preferred points of the agents and their corresponding facilities in the assignment, under the constraint of truthfulness, which ensures that agents do not misreport their mostpreferred points.We propose a resource augmentation framework, where a truthful mechanism is evaluated by its worstcase performance on an instance with enhanced facility capacities against the optimal mechanism on the same instance with the original capacities. We study a very well-known mechanism, Serial Dictatorship, and provide an exact analysis of its performance. Although Serial Dictatorship is a purely combinatorial mechanism, our analysis uses linear programming; a linear program expresses its greedy nature as well as the structure of the input, and finds the input instance that enforces the mechanism have its worst-case performance. Bounding the objective of the linear program using duality arguments allows us to compute tight bounds on the approximation ratio. Among other results, we prove that Serial Dictatorship has approximation ratio g/(g−2) when the capacities are multiplied by any integer g ≥ 3. Our results suggest that even a limited augmentation of the resources can have wondrous effects on the performance of the mechanism and in particular, the approximation ratio goes to 1 as the augmentation factor becomes large. We complement our results with bounds on the approximation ratio of Random Serial Dictatorship, the randomized version of Serial Dictatorship, when there is no resource augmentation.

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Section: Related Workmentioning

confidence: 99%

Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship

Caragiannis

Filos-Ratsikas

Frederiksen

et al. 2016

Web and Internet Economics

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“…Using the same ideas, it is not difficult to show that the (1/2)-approximation randomized algorithm of [8] implies a (1/2)-competitive algorithm in this online model. Finally, Feige and Jozeph [21] consider oblivious algorithms for Max-DiCut-algorithms in which every node is selected into the cut independently with a probability depending solely on its input and output degrees. They show a 0.483-approximation oblivious algorithm, and prove that no oblivious algorithm has an approximation ratio of 0.4899.…”

Section: Related Workmentioning

confidence: 99%

“…There exists a polynomial time 0.438-competitive algorithm for the dicut-model. Theorem 1.3 is proved by showing that an offline algorithm suggested by [21] can be implemented under the dicut-model. We complement Theorems 1.2 and 1.3 by the following theorem which gives hardness results for the dicut-model (and thus, also for the unconstrained-model).Theorem 1.4.…”

mentioning

confidence: 99%

Online Submodular Maximization with Preemption

Buchbinder¹,

Feldman²,

Schwartz³

2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

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Submodular function maximization has been studied extensively in recent years under various constraints and models. The problem plays a major role in various disciplines. We study a natural online variant of this problem in which elements arrive one-by-one and the algorithm has to maintain a solution obeying certain constraints at all times. Upon arrival of an element, the algorithm has to decide whether to accept the element into its solution and may preempt previously chosen elements. The goal is to maximize a submodular function over the set of elements in the solution.We study two special cases of this general problem and derive upper and lower bounds on the competitive ratio. Specifically, we design a 1/e-competitive algorithm for the unconstrained case in which the algorithm may hold any subset of the elements, and constant competitive ratio algorithms for the case where the algorithm may hold at most k elements in its solution.

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“…On the other hand, little is known about the limits of combinatorial approaches to Max-Di-Cut. In addition to the online inapproximation by Bar-Noy and Lampis, Feige and Jozeph [18] give a randomized oblivious algorithm 1 (where only the total in/out weights of a vertex is given) that achieves a 0.483 ratio, but show that no oblivious algorithm can do better than 0.4899. In Section 6, we discuss the relation of oblivious algorithms to our work.…”

Section: Related Workmentioning

confidence: 99%

“…Essentially, the algorithm is given full disclosure of the submodular function f andf over the set of currently revealed items. Note that in this very general model, the algorithm can potentially query exponentially many sets so that in principle such algorithms are not subject to the 1 2 inapproximation result of Feige et al [18].…”

Section: All Subsets Query (Q-type 3)mentioning

confidence: 99%

Bounds on Double-Sided Myopic Algorithms for Unconstrained Non-monotoneSubmodular Maximization

Huang

Borodin

2014

Algorithms and Computation

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Unconstrained submodular maximization captures many NP-hard combinatorial optimization problems, including Max-Cut, Max-Di-Cut, and variants of facility location problems. Recently, Buchbinder et al.[8] presented a surprisingly simple linear time randomized greedy-like online algorithm that achieves a constant approximation ratio of 1 2 , matching optimally the hardness result of Feige et al. [19]. Motivated by the algorithm of Buchbinder et al., we introduce a precise algorithmic model called double-sided myopic algorithms. We show that while the algorithm of Buchbinder et al. can be realized as a randomized online double-sided myopic algorithm, no such deterministic algorithm, even with adaptive ordering, can achieve the same approximation ratio. With respect to the Max-Di-Cut problem, we relate the Buchbinder et al. algorithm and our myopic framework to the online algorithm and inapproximation of Bar-Noy and Lampis [6].

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Oblivious Algorithms for the Maximum Directed Cut Problem

Cited by 16 publications

References 25 publications

Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship

Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship

Online Submodular Maximization with Preemption

Bounds on Double-Sided Myopic Algorithms for Unconstrained Non-monotoneSubmodular Maximization

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