A fast work function algorithm for solving the k-server problem

Rudec, Tomislav; Baumgartner, Alfonzo; Manger, Robert

doi:10.1007/s10100-011-0222-7

Cited by 21 publications

(26 citation statements)

References 13 publications

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“…Euclidean distance (i.e., traveled distance) is used to measure the commuting cost between two locations for all datasets. We use the window version of WFA [15] (i.e., ω-WFA) in the experiments considering the running time. We evaluate the 50-WFA on the Delivery data where there is 1 task per step and m = {50, 100, 200}.…”

Section: Experimental Methodologymentioning

confidence: 99%

Cost Minimization and Social Fairness for Spatial Crowdsourcing Tasks

Liu¹,

Abdessalem²,

Wu³

et al. 2016

Database Systems for Advanced Applications

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Spatial crowdsourcing is an activity consisting in outsourcing spatial tasks to a community of online, yet on-ground and mobile, workers. A spatial task is characterized by the requirement that workers must move from their current location to a specified location to accomplish the task. We study the assignment of spatial tasks to workers. A sequence of sets of spatial tasks is assigned to workers as they arrive. We want to minimize the cost incurred by the movement of the workers to perform the tasks. In the meanwhile, we are seeking solutions that are socially fair. We discuss the competitiveness in terms of competitive ratio and social fairness of the Work Function Algorithm, the Greedy Algorithm, and the Randomized versions of the Greedy Algorithm to solve this problem. These online algorithms are memory-less and are either inefficient or unfair. In this paper, we devise two Distribution Aware Algorithms that utilize the distribution information of the tasks and that assign tasks to workers on the basis of the learned distribution. With realistic and synthetic datasets, we empirically and comparatively evaluate the performance of the three baseline and two Distribution Aware Algorithms.

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Section: Experimental Methodologymentioning

confidence: 99%

Cost Minimization and Social Fairness for Spatial Crowdsourcing Tasks

Liu¹,

Abdessalem²,

Wu³

et al. 2016

Database Systems for Advanced Applications

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“…Moreover, [18] presents experimental data that show that greedy is relatively close in performance to the offline optimal algorithm on the line. Similar experiments, for a variety of metric spaces and algorithms, including greedy, are presented in [10,40,41]. In a related work, Anagnostopoulos et al [2] studied the steady-state distribution of greedy for the k-server problem on the circle.…”

Section: Related Work and Preliminariesmentioning

confidence: 99%

Stochastic Dominance and the Bijective Ratio of Online Algorithms

Angelopoulos

Schweitzer

2019

Algorithmica

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Stochastic dominance is a technique for evaluating the performance of online algorithms that provides an intuitive, yet powerful stochastic order between the compared algorithms. Accordingly this holds for bijective analysis, which can be interpreted as stochastic dominance assuming the uniform distribution over requests. These techniques have been applied in problems such as paging, list update, bin coloring, routing in array mesh networks, and in connection with Bloom filters, and have provided a clear separation between algorithms whose performance varies significantly in practice. However, despite their appealing properties, there are situations in which they are not readily applicable. This is due to the fact that they stipulate a stringent relation between the compared algorithms that may be either too difficult to establish analytically, or worse, may not even exist.In this paper we propose remedies to both of these shortcomings. First, we establish sufficient conditions that allow us to prove the bijective optimality of a certain class of algorithms for a wide range of problems; we demonstrate this approach in the context of well-studied online problems such as weighted paging, reordering buffer management, and 2-server on the circle. Second, to account for situations in which two algorithms are incomparable or there is no clear optimum, we introduce the bijective ratio as a natural extension of (exact) bijective analysis. Our definition readily generalizes to stochastic dominance. This renders the concept of bijective analysis (and that of stochastic dominance) applicable to all online problems, is a broad generalization of the Max/Max ratio due to Ben-David and Borodin, and allows for the incorporation of other useful techniques such as amortized analysis. We demonstrate the applicability of the bijective ratio to one of the fundamental online problems, namely the continuous k-server problem on metrics such as the line, the circle, and the star. Among other results, we show that the greedy algorithm attains bijective ratios of O(k) consistently across these metrics. These results confirm extensive previous studies that gave evidence of the efficiency of this algorithm on said metrics in practice, which, however, is not reflected in competitive analysis.

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“…For general metrics, the best known result is the Work-Function algorithm, which is shown to be 2k − 1-competitive [16]. Although this algorithm seems generally inefficient with respect to runtime and memory, there have been studies showing that an efficient implementation of this algorithm is indeed possible [19,20]. It was also shown that the algorithm has an optimal competitive ratio of k on line and star metrics, as well as metrics with k + 2 points [5].…”

Section: Related Workmentioning

confidence: 99%

Managing Multiple Mobile Resources

et al. 2021

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We extend the Mobile Server problem introduced in Feldkord and Meyer auf der Heide (TOPC 6(3), 14:1–14:17 2019) to a model where k identical mobile resources, here named servers, answer requests appearing at points in the Euclidean space. To reduce communication costs, the positions of the servers can be adapted by a limited distance ms per round for each server. The costs are measured similarly to the classical Page Migration problem: i.e., answering a request induces costs proportional to the distance to the nearest server, and moving a server induces costs proportional to the distance multiplied with a weight D. We show that, in our model, no online algorithm can have a constant competitive ratio: i.e., one which is independent of the input length n, even if an augmented moving distance of (1 + δ)ms is allowed for the online algorithm. Therefore we investigate a restriction of the power of the adversary dictating the sequence of requests: We demand locality of requests: i.e., that consecutive requests come from points in the Euclidean space with distance bounded by some constant mc. We show constant lower bounds on the competitiveness in this setting (independent of n, but dependent on k, ms and mc). On the positive side, we present a deterministic online algorithm with bounded competitiveness when an augmented moving distance and locality of requests is assumed. Our algorithm simulates any given algorithm for the classical k-Page Migration problem as guidance for its servers and extends it by a greedy move of one server in every round. The resulting competitive ratio is polynomial in the number of servers k, the ratio between mc and ms, the inverse of the augmentation factor 1/δ and the competitive ratio of the simulated k-Page Migration algorithm. We also show how to directly adapt the Double Coverage algorithm (Chrobak et al. SIAM J. Discrete Math. 4(2), 172–181 11) for the k-Server problem to receive an algorithm with improved competitiveness on the line.

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A fast work function algorithm for solving the k-server problem

Cited by 21 publications

References 13 publications

Cost Minimization and Social Fairness for Spatial Crowdsourcing Tasks

Cost Minimization and Social Fairness for Spatial Crowdsourcing Tasks

Stochastic Dominance and the Bijective Ratio of Online Algorithms

Managing Multiple Mobile Resources

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