Efficient Many-To-Many Point Matching in One Dimension

  • Authors:

  • Justin Colannino;Mirela Damian;Ferran Hurtado;Stefan Langerman;Henk Meijer;Suneeta Ramaswami;Diane Souvaine;Godfried Toussaint

  • Affiliations:

  • McGill University, School of Computer Science, Montreal, QC, Canada;Villanova University, Department of Computer Science, Villanova, PA, USA;Universitat Politècnica de Catalunya, Departament de Matemàtica Aplicada II, Barcelona, PA, Spain;Université Libre de Bruxelles, Chercheur qualifié du FNRS, Département d’ Informatique, Brussels, PA, Belgium;Queen’s University, School of Computing, Kingston, PA, Canada;Rutgers University, Department of Computer Science, 08102, Camden, NJ, USA;Tufts University, Department of Computer Science, 08102, Medford, NJ, USA;McGill University, School of Computer Science and Centre for Interdisciplinary Research in Music Media and Technology (CIRMMT), The Schulich School of Music, 08102, Montreal, NJ, Canada

  • Venue:
  • Graphs and Combinatorics
  • Year:
  • 2007

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Abstract

Let S and T be two sets of points with total cardinality n. The minimum-cost many-to-many matching problem matches each point in S to at least one point in T and each point in T to at least one point in S, such that sum of the matching costs is minimized. Here we examine the special case where both S and T lie on the line and the cost of matching s ∈S to t ∈T is equal to the distance between s and t. In this context, we provide an algorithm that determines a minimum-cost many-to-many matching in O(n log n) time, improving the previous best time complexity of O(n2) for the same problem.