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Improved online algorithms for the sorting buffer problem on line metrics

Authors:

Iftah Gamzu,

Danny SegevAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 6, Issue 1

Article No.: 15, Pages 1 - 14

https://doi.org/10.1145/1644015.1644030

Published: 28 December 2009 Publication History

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Abstract

An instance of the sorting buffer problem consists of a metric space and a server, equipped with a finite-capacity buffer capable of holding a limited number of requests. An additional ingredient of the input is an online sequence of requests, each of which is characterized by a destination in the given metric space; whenever a request arrives, it must be stored in the sorting buffer. At any point in time, a currently pending request can be served by drawing it out of the buffer and moving the server to its corresponding destination. The objective is to serve all input requests in a way that minimizes the total distance traveled by the server.

In this article, we focus our attention on instances of the problem in which the underlying metric is either an evenly-spaced line metric or a continuous line metric. Our main findings can be briefly summarized as follows.

(1) We present a deterministic O(log n)-competitive algorithm for n-point evenly-spaced line metrics. This result improves on a randomized O(log² n)-competitive algorithm due to Khandekar and Pandit [2006b]. It also refutes their conjecture, stating that a deterministic strategy is unlikely to obtain a nontrivial competitive ratio.

(2) We devise a deterministic O(log N log log N)-competitive algorithm for continuous line metrics, where N denotes the length of the input sequence. In this context, we introduce a novel discretization technique of independent interest.

(3) We establish the first nontrivial lower bound for the evenly-spaced case, by proving that the competitive ratio of any deterministic algorithm is at least 2 + √3/√3 ≈ 2.154. This result settles, to some extent, an open question due to Khandekar and Pandit [2006b], who posed the task of attaining lower bounds on the achievable competitive ratio as a foundational objective for future research.

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Cited By

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Adamaszek ACzumaj AEnglert MRäcke H(2022)Almost Tight Bounds for Reordering Buffer ManagementSIAM Journal on Computing10.1137/20M132616751:3(701-722)Online publication date: 24-May-2022
https://doi.org/10.1137/20M1326167
Englert MRacke HStotz R(2019)Polylogarithmic Guarantees for Generalized Reordering Buffer Management2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2019.00012(38-59)Online publication date: Nov-2019
https://doi.org/10.1109/FOCS.2019.00012
Englert M(2018)The reordering buffer problem on the line revisitedACM SIGACT News10.1145/3197406.319741849:1(67-72)Online publication date: 14-Mar-2018
https://dl.acm.org/doi/10.1145/3197406.3197418
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Index Terms

Improved online algorithms for the sorting buffer problem on line metrics
1. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Scheduling algorithms
    2. Online algorithms
      1. Online learning algorithms
        Scheduling algorithms
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Reinforcement learning
        Sequential decision making

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 6, Issue 1

December 2009

374 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1644015

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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 December 2009

Accepted: 01 November 2008

Revised: 01 May 2008

Received: 01 January 2007

Published in TALG Volume 6, Issue 1

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Adamaszek ACzumaj AEnglert MRäcke H(2022)Almost Tight Bounds for Reordering Buffer ManagementSIAM Journal on Computing10.1137/20M132616751:3(701-722)Online publication date: 24-May-2022
https://doi.org/10.1137/20M1326167
Englert MRacke HStotz R(2019)Polylogarithmic Guarantees for Generalized Reordering Buffer Management2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2019.00012(38-59)Online publication date: Nov-2019
https://doi.org/10.1109/FOCS.2019.00012
Englert M(2018)The reordering buffer problem on the line revisitedACM SIGACT News10.1145/3197406.319741849:1(67-72)Online publication date: 14-Mar-2018
https://dl.acm.org/doi/10.1145/3197406.3197418
Bienkowski MBöhm MJeż ŁLaskoś-Grabowski PMarcinkowski JSgall JSpyra AVeselý P(2018)Logarithmic price of buffer downscaling on line metricsTheoretical Computer Science10.1016/j.tcs.2017.10.008707(89-93)Online publication date: Jan-2018
https://doi.org/10.1016/j.tcs.2017.10.008
Bienkowski MKraska ASchmidt P(2018)Online Service with Delay on a LineStructural Information and Communication Complexity10.1007/978-3-030-01325-7_22(237-248)Online publication date: 31-Oct-2018
https://doi.org/10.1007/978-3-030-01325-7_22
Englert MRäcke HKlein P(2017)Reordering buffers with logarithmic diameter dependency for treesProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039765(1224-1234)Online publication date: 16-Jan-2017
https://dl.acm.org/doi/10.5555/3039686.3039765
Azar YGanesh AGe RPanigrahi DHatami HMcKenzie PKing V(2017)Online service with delayProceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3055399.3055475(551-563)Online publication date: 19-Jun-2017
https://dl.acm.org/doi/10.1145/3055399.3055475
Englert MWestermann M(2016)Scheduling with a Reordering BufferEncyclopedia of Algorithms10.1007/978-1-4939-2864-4_502(1905-1910)Online publication date: 22-Apr-2016
https://doi.org/10.1007/978-1-4939-2864-4_502
Avigdor-Elgrabli NRabani Y(2015)An Improved Competitive Algorithm for Reordering Buffer ManagementACM Transactions on Algorithms10.1145/266334711:4(1-15)Online publication date: 23-Jun-2015
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Avigdor-Elgrabli NIm SMoseley BRabani Y(2015)On the Randomized Competitive Ratio of Reordering Buffer Management with Non-Uniform CostsAutomata, Languages, and Programming10.1007/978-3-662-47672-7_7(78-90)Online publication date: 20-Jun-2015
https://doi.org/10.1007/978-3-662-47672-7_7
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