Improved online algorithms for the sorting buffer problem

Iftah Gamzu, Danny Segev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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; 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 paper, we focus our attention on instances of the problem in which the underlying metric is either an evenly-spaced 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. 2. We devise a deterministic O(log N log log N) competitive algorithm for continuous line metrics, where N is the input sequence length. 3. We establish the first non-trivial 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.

Original languageEnglish
Title of host publicationSTACS 2007 - 24th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings
PublisherSpringer Verlag
Pages658-669
Number of pages12
ISBN (Print)9783540709176
DOIs
StatePublished - 2007
Event24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007 - Aachen, Germany
Duration: 22 Feb 200724 Feb 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4393 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007
Country/TerritoryGermany
CityAachen
Period22/02/0724/02/07

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