New Ressults on Server Problems

Chrobák, Marek; Karloff, Howard; Payne, Tom; Vishwanathan, Sundar

doi:10.1137/0404017

Cited by 210 publications

(161 citation statements)

References 7 publications

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“…This generalizes the previous results for h = k [3,4]. Our proof also follows similar ideas, but our potential function is more involved (it has three terms instead of two), and the analysis is more subtle.…”

Section: Theorem 2 For Any Tree the Competitive Ratio Of DC Is At Mosupporting

confidence: 82%

“…Note this generalizes the potential considered in [3,4] for the case of h = k. In that setting, all the online servers are matched and hence D M = D X and is independent of M, and thus the potential above becomes k times that minimum cost matching between X and Y plus D x . On the other hand in our setting, we need to select the right set M of DC servers to be matched to the offline servers based on minimizing…”

Section: Upper Boundmentioning

confidence: 58%

“…The conjecture has been settled for several special metrics (an excellent reference is [2]). In particular for the line metric, Chrobak et al [3] gave an elegant k-competitive algorithm called Double Coverage (DC). This algorithm was later extended and shown to be k-competitive for all tree metrics [4].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, we consider the DC algorithm [3] originally defined for a line, and its generalization to trees [4]. We refer to both as DC, since the latter specializes to the former when the underlying tree is in fact a line.…”

Section: Introductionmentioning

confidence: 99%

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Tight Bounds for Double Coverage Against Weak Adversaries

et al. 2016

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We study the Double Coverage (DC) algorithm for the k-server problem in tree metrics in the (h, k)-setting, i.e., when DC with k servers is compared against an offline optimum algorithm with h ≤ k servers. It is well-known that in such metric spaces DC is k-competitive (and thus optimal) for h = k. We prove that even if k > h the competitive ratio of DC does not improve; in fact, it increases slightly as k grows, tending to h + 1. Specifically, we give matching upper and lower bounds of k(h+1) k+1 on the competitive ratio of DC on any tree metric.

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Section: Theorem 2 For Any Tree the Competitive Ratio Of DC Is At Mosupporting

confidence: 82%

Section: Upper Boundmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tight Bounds for Double Coverage Against Weak Adversaries

et al. 2016

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“…This has led us to the development of an online algorithm that is both lazy and non-marking. Unfortunately for us, we later discovered that this algorithm already appears as ROTATE in [CKPV91], where it is proved to be k-competitive, by means of amortized analysis. Below we give a brief description of FWF and ROTATE.…”

Section: Symbolic Model-checking Algorithmmentioning

confidence: 99%

Formal Analysis of Online Algorithms

Aminof

Kupferman

Lampert

2011

Automated Technology for Verification and Analysis

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Abstract. In [AKL10], we showed how viewing online algorithms as reactive systems enables the application of ideas from formal verification to the competitive analysis of online algorithms. Our approach is based on weighted automata, which assign to each input word a cost in IR ≥0 . By relating the "unbounded look ahead" of optimal offline algorithms with nondeterminism, and relating the "no look ahead" of online algorithms with determinism, we were able to solve problems about the competitive ratio of online algorithms and the memory they require. In this paper we improve the application in three important and technically challenging aspects. First, we allow the competitive analysis to take into account assumptions about the environment. Second, we allow the online algorithm to have a bounded lookahead. Third, we describe a symbolic version of the model-checking algorithm and demonstrate its applicability. The first two contributions broaden the scope of our approach to settings in which the traditional analysis of online algorithms is particularly complicated. The third contribution improves the practicality of our approach and enables it to handle larger state spaces.

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