A o(n)-Competitive Deterministic Algorithm for Online Matching on a Line

Online matching on a line involves matching an online stream of items of various sizes to stored items of various sizes, with the objective of minimizing the average discrepancy in size between matched items. The best previously known upper and lower bounds on the optimal deterministic competitive r...

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Bibliographic Details
Published inApproximation and Online Algorithms Vol. 8952; pp. 11 - 22
Main Authors Antoniadis, Antonios, Barcelo, Neal, Nugent, Michael, Pruhs, Kirk, Scquizzato, Michele
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 01.01.2015
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Algorithms & data structures
Competitive Ratio
Deterministic Algorithm
Discrete mathematics
Mathematical theory of computation
Online Algorithm
Optimal Match
Search Problem
Online AccessGet full text
ISBN9783319182629
3319182625
ISSN0302-9743
1611-3349
DOI10.1007/978-3-319-18263-6_2

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Summary:Online matching on a line involves matching an online stream of items of various sizes to stored items of various sizes, with the objective of minimizing the average discrepancy in size between matched items. The best previously known upper and lower bounds on the optimal deterministic competitive ratio are linear in the number of items, and constant, respectively. We show that online matching on a line is essentially equivalent to a particular search problem, that we call $$k$$ -lost cows. We then obtain the first deterministic sub-linearly competitive algorithm for online matching on a line by giving such an algorithm for the $$k$$ -lost cows problem.
Bibliography:A. Antoniadis—Part of the work was done while the author was at the University of Pittsburgh, supported by a fellowship within the Postdoc-Programme of the German Academic Exchange Service (DAAD). N. Barcelo—This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1247842. K. Pruhs—Supported in part by NSF grants CCF-1115575, CNS-1253218, CCF-1421508, and an IBM Faculty Award. M. Scquizzato—Work done while at the University of Pittsburgh, supported in part by a fellowship of “Fondazione Ing. Aldo Gini”, University of Padova.
Original Title: A \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$o(n)$$\end{document}-Competitive Deterministic Algorithm for Online Matching on a Line
Original Abstract: Online matching on a line involves matching an online stream of items of various sizes to stored items of various sizes, with the objective of minimizing the average discrepancy in size between matched items. The best previously known upper and lower bounds on the optimal deterministic competitive ratio are linear in the number of items, and constant, respectively. We show that online matching on a line is essentially equivalent to a particular search problem, that we call \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-lost cows. We then obtain the first deterministic sub-linearly competitive algorithm for online matching on a line by giving such an algorithm for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-lost cows problem.
ISBN:9783319182629
3319182625
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-18263-6_2