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The Euclidean Matching Problem

  • Gabriele Sicuro

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Gabriele Sicuro
    Pages 1-4
  3. Gabriele Sicuro
    Pages 5-23
  4. Gabriele Sicuro
    Pages 59-118
  5. Gabriele Sicuro
    Pages 119-120
  6. Back Matter
    Pages 121-136

About this book

Introduction

This thesis discusses the random Euclidean bipartite matching problem, i.e., the matching problem between two different sets of points randomly generated on the Euclidean domain. The presence of both randomness and Euclidean constraints makes the study of the average properties of the solution highly relevant. The thesis reviews a number of known results about both matching problems and Euclidean matching problems. It then goes on to provide a complete and general solution for the one dimensional problem in the case of convex cost functionals and, moreover, discusses a potential approach to the average optimal matching cost and its finite size corrections in the quadratic case. The correlation functions of the optimal matching map in the thermodynamical  limit are also analyzed. Lastly, using a functional approach, the thesis puts forward a general recipe for the computation of the correlation function of the optimal matching in any dimension and in a generic domain.
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Keywords

Bipartite Matching Problem Cavity Method Replica Trick Euclidean Optimization Problem Random Optimization Problem Euclidean Matching Problem Convex Cost Functionals

Authors and affiliations

  • Gabriele Sicuro
    • 1
  1. 1.Centro Brasileiro de Pesquisas FísicasRio de JaneiroBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-46577-7
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-46576-0
  • Online ISBN 978-3-319-46577-7
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • Buy this book on publisher's site
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