The 3-server problem in the plane

Bein, Wolfgang; Chrobák, Marek; Larmore, Lawrence L.

doi:10.1016/s0304-3975(01)00305-x

Cited by 24 publications

(19 citation statements)

References 10 publications

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“…The conjecture is true for k = 2, for the line [3], trees [4], and on fixed k + 1 or k + 2 points [5]. It is still open for the 3-server problem on more than six points and also on the circle [6]. The lower bound is k which is shown in the original paper [1].…”

Section: Introductionmentioning

confidence: 93%

Randomized Competitive Analysis for Two Server Problems

2008

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Section: Introductionmentioning

confidence: 93%

Randomized Competitive Analysis for Two Server Problems

2008

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“…Our (3 + 1/D)-competitive algorithm is a typical work function algorithm similar to algorithms for metrical task systems, e.g., [9], and k-server problems [5,12]. In general, a work function algorithm makes online decisions using information on the optimal offline cost for processing requests that have been issued so far and ending at each configuration (page node in the page migration problem).…”

Section: Overview Of Technical Ideasmentioning

confidence: 99%

“…The purpose of considering such a decline on the work function as a trigger of migration is to avoid requests onŝ that would increase online service cost at the server s but change neither OPT s nor OPTŝ. A similar idea is used for other work function algorithms ( [9,5,12]). We prove the following theorem:…”

Section: Preliminariesmentioning

confidence: 99%

Asymptotically Optimal Online Page Migration on Three Points

Matsubayashi

2013

Algorithmica

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This paper addresses the page migration problem: given online requests from nodes on a network for accessing a page stored in a node, output online migrations of the page. Serving a request costs the distance between the request and the page, and migrating the page costs the migration distance multiplied by the page size D ≥ 1. The objective is to minimize the total sum of service costs and migration costs. Black and Sleator conjectured that there exists a 3-competitive deterministic algorithm for every graph. Although the conjecture was disproved for the case D = 1, whether or not an asymptotically (with respect to D) 3-competitive deterministic algorithm exists for every graph is still open. In fact, we did not know if there exists a 3-competitive deterministic algorithm for an extreme case of three nodes with D ≥ 2. As the first step toward an asymptotic version of the Black and Sleator conjecture, we present 3-and (3 + 1/D)-competitive algorithms on three nodes with D = 2 and D ≥ 3, respectively, and a lower bound of 3 + Ω (1/D) that is greater than 3 for every D ≥ 3. In addition to the results on three nodes, we also derive ρ-competitiveness on complete graphs with edge-weights between 1 and 2 − 2/ρ for any ρ ≥ 3, extending the previous 3-competitive algorithm on uniform networks.

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“…However, k-competitive on-line algorithms are known for some special cases. Examples are line [14], tree metric spaces [15], any metric space with n = k + 1 [16,25] or n = k + 2 [6,24], manhattan plane with k = 3 [7], etc.…”

Section: Definition 1 An On-line Algorithm a For The K-server Problementioning

confidence: 99%

A randomized on–line algorithm for the k–server problem on a line

Csaba

Lodha

2006

Random Struct Algorithms

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ABSTRACT:The k-server problem is one of the most important and well-studied problems in the area of on-line computation. Its importance stems from the fact that it models many practical problems like multi-level memory paging encountered in operating systems, weighted caching used in the management of web caches, head motion planning of multi-headed disks, and robot motion planning. In this paper, we investigate its randomized version for which (log k)-competitiveness is conjectured and yet hardly any

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The 3-server problem in the plane

Cited by 24 publications

References 10 publications

Randomized Competitive Analysis for Two Server Problems

Randomized Competitive Analysis for Two Server Problems

Asymptotically Optimal Online Page Migration on Three Points

A randomized on–line algorithm for the k–server problem on a line

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