Buying a Constant Competitive Ratio for Paging

Csirik, János; Imreh, Csanád; Noga, John; Seiden, Steven S.; Woeginger, Gerhard J.

doi:10.1007/3-540-44676-1_8

Cited by 4 publications

(10 citation statements)

References 7 publications

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“…In Section 3 we present upper and lower bounds on the competitive ratio of the infinite server problem on a variety of metric spaces. Extending the work in [10], we present a tight lower bound for non-discrete spaces, which is then turned into a 3.146 lower bound for the (h, k) setting. To our knowledge, this is the largest bound on the weak adversaries setting for any metric space, as k/h → ∞.…”

Section: Our Resultsmentioning

confidence: 99%

“…The closest publication to this work is by Csirik et al [10], which studies a problem that is essentially the special case of the infinite server problem on the uniform metric space augmented by a far away source. It is cast as a paging problem where new cache slots can be bought at a fixed price per unit and gives matching upper and lower bounds of ≈ 3.146 on the competitive ratio.…”

Section: Previous Workmentioning

confidence: 99%

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The Infinite Server Problem

Coester¹,

Koutsoupias²,

Lazos³

2017

Preprint

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We study a variant of the k-server problem, the infinite server problem, in which infinitely many servers reside initially at a particular point of the metric space and serve a sequence of requests. In the framework of competitive analysis, we show a surprisingly tight connection between this problem and the (h, k)-server problem, in which an online algorithm with k servers competes against an offline algorithm with h servers. Specifically, we show that the infinite server problem has bounded competitive ratio if and only if the (h, k)-server problem has bounded competitive ratio for some k = O(h). We give a lower bound of 3.146 for the competitive ratio of the infinite server problem, which implies the same lower bound for the (h, k)-server problem even when k/h → ∞ and holds also for the line metric; the previous known bounds were 2.4 for general metric spaces and 2 for the line. For weighted trees and layered graphs we obtain upper bounds, although they depend on the depth. Of particular interest is the infinite server problem on the line, which we show to be equivalent to the seemingly easier case in which all requests are in a fixed bounded interval away from the original position of the servers. This is a special case of a more general reduction from arbitrary metric spaces to bounded subspaces. Unfortunately, classical approaches (double coverage and generalizations, work function algorithm, balancing algorithms) fail even for this special case. * Supported by the ERC Advanced Grant 321171 (ALGAME) and by EPSRC. 1 We first learned about this problem from Kamal Jain [14].

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Section: Our Resultsmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

The Infinite Server Problem

Coester¹,

Koutsoupias²,

Lazos³

2017

Preprint

View full text Add to dashboard Cite

show abstract

“…The expression min {opt s ( , ) + } can be seen as the optimal cost in a model where one has to buy the servers, for a cost of each. This problem on uniform spaces was studied in [11]. In this case D s ( ) is the number of servers bought in an optimal solution.…”

Section: Discussionmentioning

confidence: 98%

“…Starting from the PARTITION algorithm [15] and iterating Theorem 8 we get the following result: In [11] a model has been investigated, where one does not have a fixed number of servers but they can be bought. The expression min {opt s ( , ) + } can be seen as the optimal cost in a model where one has to buy the servers, for a cost of each.…”

Section: Discussionmentioning

confidence: 98%

Randomized algorithm for the k-server problem on decomposable spaces

Nagy-György

2009

Journal of Discrete Algorithms

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We study the randomized k-server problem on metric spaces consisting of widely separated subspaces. We give a method which extends existing algorithms to larger spaces with the growth rate of the competitive quotients being at most O (log k). This method yields o(k)-competitive algorithms solving the randomized k-server problem for some special underlying metric spaces, e.g. HSTs of "small" height (but unbounded degree). HSTs are important tools for probabilistic approximation of metric spaces.

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“…In [4] the generalized version of the paging problem is investigated. In that paper the cost of purchasing extra memory is described by an arbitrary cost function.…”

Section: Introductionmentioning

confidence: 99%

Online scheduling with general machine cost functions

Imreh

2009

Discrete Applied Mathematics

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For most scheduling problems the set of machines is fixed initially and remains unchanged for the duration of the problem.Recently online scheduling problems have been investigated with the modification that initially the algorithm possesses no machines, but that at any point additional machines may be purchased. In all of these models the assumption has been made that each machine has unit cost. In this paper we consider the problem with general machine cost functions. Furthermore we also consider a more general version of the problem where the available machines have speed, the algorithm may purchase machines with speed 1 and machines with speed s. We define and analyze some algorithms for the solution of these problems and their special cases. Moreover we prove some lower bounds on the possible competitive ratios.

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Buying a Constant Competitive Ratio for Paging

Cited by 4 publications

References 7 publications

The Infinite Server Problem

The Infinite Server Problem

Randomized algorithm for the k-server problem on decomposable spaces

Online scheduling with general machine cost functions

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