The -server problem

Koutsoupias, Elias

doi:10.1016/j.cosrev.2009.04.002

Cited by 93 publications

(69 citation statements)

References 69 publications

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“…For weighted k-server problem, in which servers have different weights and the cost for a server to serve a request is equal to moving distance times its weight, Chrobak and Sgall [3] proved the work function algorithm was 5-competitive for 2-server in a uniform space, in which the distance between any two points is a unit. As referred to, since the k-server problem is critical and has long history, please see [5] for a detailed survey.…”

Section: B Related Work and Their Resultsmentioning

confidence: 99%

An improved model to efficiently transport YouBike

2014

Proceedings of the 11th IEEE International Conference on Networking, Sensing and Control

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For energy conservation and reduction of carbon emissions, an eco-friendly public transportation system is in dispensable in a modern country. Since a bicycle itself is a low-population and low-energy-consumption vehicle, many cities, including Taipei, have built a convenient public bicycle sharing system as an extension of the metro system to follow the trend.YouBike, a corresponding system in Taipei, has become more and more popular and pervasive recently. In practice, a commuter can rent a bicycle in a rental station. Once some rental station is out-of bicycles, it will automatically inform the management system and the system has to transport bicycles from other station or depository to supply it. From the viewpoint of commuters, they would like to obtain a bicycle as soon as possible; however, from the perspective of a manager, not only the utilization of the system, but also the transportation cost, is critical to maintain the operation. Hence how to address the online optimization problem and balance the bi-criteria issue is a hot topic. In [6], Li and Liu borrowed the k-server problem [9] to deliver a theoretical model to address this problem. Nonetheless, their model has some drawbacks that are insufficient to approach the real case. In this paper, we add new elements to improve their model and formally define the YouBike transport problem. Moreover, we consider this problem in a uniform space to further explore its inner properties and solution hardship. Finally, some indications for future works are also presented.Keywords--online algorithm, the k-server problem, YouBike, public bicycle sharing system

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Section: B Related Work and Their Resultsmentioning

confidence: 99%

An improved model to efficiently transport YouBike

2014

Proceedings of the 11th IEEE International Conference on Networking, Sensing and Control

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“…Subsequently, Chung et al [3] gave a polylogarithmic algorithm for the variant where the algorithm has one additional server at every point in the metric where there is at least one server. Another problem which resembles online matching is the k-server problem (see [9] for a survey). The main difference between the two problems is that in the k-server problem a server can be used to serve subsequent requests, while in the online matching problem a server has to be irrevocably matched to a request.…”

Section: Other Related Problemsmentioning

confidence: 99%

A Collection of Lower Bounds for Online Matching on the Line

Antoniadis

Fischer

Tönnis

2018

LATIN 2018: Theoretical Informatics

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In the online matching on the line problem, the task is to match a set of requests R online to a given set of servers S. The distance metric between any two points in R ∪ S is a line metric and the objective for the online algorithm is to minimize the sum of distances between matched server-request pairs. This problem is well-studied and -despite recent improvements -there is still a large gap between the best known lower and upper bounds: The best known deterministic algorithm for the problem is O(log 2 n)-competitive, while the best known deterministic lower bound is 9.001. The lower and upper bounds for randomized algorithms are 4.5 and O(log n) respectively.We prove that any deterministic online algorithm which in each round: (i) bases the matching decision only on information local to the current request, and (ii) is symmetric (in the sense that the decision corresponding to the mirror image of some instance I is the mirror image of the decision corresponding to instance I), must be Ω(log n)-competitive. We then extend the result by showing that it also holds when relaxing the symmetry property so that the algorithm might prefer one side over the other, but only up to some degree. This proves a barrier of Ω(log n) on the competitive ratio for a large class of "natural" algorithms. This class includes all deterministic online algorithms found in the literature so far.Furthermore, we show that our result can be extended to randomized algorithms that locally induce a symmetric distribution over the chosen servers. The Ω(log n)-barrier on the competitive ratio holds for this class of algorithms as well.

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“…The k-server problem was introduced by Manasse, McGeoch, and Sleater [15]. A review of the k-server problem literature was written by Koutsoupias [13]. For randomized algorithms in discrete metrics, the competitive ratio O(log 2 (k) log (n)) was attained by Bubeck et.…”

Section: Related Workmentioning

confidence: 99%

DISPATCH: An Optimally-Competitive Algorithm for Maximum Online Perfect Bipartite Matching with i.i.d. Arrivals

Chang

Spaen

Velednitsky

2018

Approximation and Online Algorithms

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This work presents an optimally-competitive algorithm for the problem of maximum weighted online perfect bipartite matching with i.i.d. arrivals. In this problem, we are given a known set of workers, a distribution over job types, and non-negative utility weights for each pair of worker and job types. At each time step, a job is drawn i.i.d. from the distribution over job types. Upon arrival, the job must be irrevocably assigned to a worker and cannot be dropped. The goal is to maximize the expected sum of utilities after all jobs are assigned. We introduce Dispatch, a 0.5-competitive, randomized algorithm. We also prove that 0.5-competitive is the best possible. Dispatch first selects a "preferred worker" and assigns the job to this worker if it is available. The preferred worker is determined based on an optimal solution to a fractional transportation problem. If the preferred worker is not available, Dispatch randomly selects a worker from the available workers. We show that Dispatch maintains a uniform distribution over the workers even when the distribution over the job types is non-uniform.

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The -server problem

Cited by 93 publications

References 69 publications

An improved model to efficiently transport YouBike

An improved model to efficiently transport YouBike

A Collection of Lower Bounds for Online Matching on the Line

DISPATCH: An Optimally-Competitive Algorithm for Maximum Online Perfect Bipartite Matching with i.i.d. Arrivals

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