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On the bicriteria k-server problem

Published: 08 December 2010 Publication History

Abstract

In this article we consider multicriteria formulations of classical online problems in which an algorithm must simultaneously perform well with respect to two different cost measures. Every strategy for serving a sequence of requests is characterized by a pair of costs and therefore there can be many different minimal or optimal incomparable solutions. The adversary is assumed to choose from one of these minimal strategies and the performance of the algorithm is measured with respect to the costs the adversary pays servicing the sequence according to its determined choice of strategy. We consider a parametric family of functions which includes all the possible selections for such strategies. Then, starting from a simple general method that combines any multicriteria instance into a single-criterion one, we provide a universal multicriteria algorithm that can be applied to different online problems. In the multicriteria k-server formulation with two different edge weightings, for each function class, such a universal algorithm achieves competitive ratios that are only an O(log W) multiplicative factor away from the corresponding determined lower bounds, where W is the maximum ratio between the two weights associated to each edge. We then extend our results to two specific functions, for which nearly optimal competitive algorithms are obtained by exploiting more knowledge of the selection properties. Finally, we show how to apply our framework to other multicriteria online problems sharing similar properties.

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Cited By

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  • (2019)A new approach to solve the k-server problem based on network flows and flow cost reductionComputers and Operations Research10.1016/j.cor.2012.11.00640:4(1004-1013)Online publication date: 4-Jan-2019
  • (2014)A fast approximate implementation of the work function algorithm for solving the $$k$$ k -server problemCentral European Journal of Operations Research10.1007/s10100-014-0349-423:3(699-722)Online publication date: 27-Apr-2014

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  1. On the bicriteria k-server problem

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    Published In

    cover image ACM Transactions on Algorithms
    ACM Transactions on Algorithms  Volume 7, Issue 1
    November 2010
    282 pages
    ISSN:1549-6325
    EISSN:1549-6333
    DOI:10.1145/1868237
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 08 December 2010
    Accepted: 01 December 2009
    Revised: 01 December 2009
    Received: 01 September 2008
    Published in TALG Volume 7, Issue 1

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    Author Tags

    1. k-server problem
    2. Online algorithms
    3. bicriteria optimization

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    • (2019)A new approach to solve the k-server problem based on network flows and flow cost reductionComputers and Operations Research10.1016/j.cor.2012.11.00640:4(1004-1013)Online publication date: 4-Jan-2019
    • (2014)A fast approximate implementation of the work function algorithm for solving the $$k$$ k -server problemCentral European Journal of Operations Research10.1007/s10100-014-0349-423:3(699-722)Online publication date: 27-Apr-2014

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