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Efficient Many-To-Many Point Matching in One Dimension

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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.

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Authors and Affiliations

  1. School of Computer Science, McGill University, Montreal, QC, Canada

    Justin Colannino

  2. Department of Computer Science, Villanova University, Villanova, PA, USA

    Mirela Damian

  3. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain

    Ferran Hurtado

  4. Chercheur qualifié du FNRS, Département d’ Informatique, Université Libre de Bruxelles, Brussels, Belgium

    Stefan Langerman

  5. School of Computing, Queen’s University, Kingston, Canada

    Henk Meijer

  6. Department of Computer Science, Rutgers University, Camden, NJ, 08102, USA

    Suneeta Ramaswami

  7. Department of Computer Science, Tufts University, Medford, USA

    Diane Souvaine

  8. School of Computer Science and Centre for Interdisciplinary Research in Music Media and Technology (CIRMMT), The Schulich School of Music, McGill University, Montreal, Canada

    Godfried Toussaint

Authors
  1. Justin Colannino
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  2. Mirela Damian
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  3. Ferran Hurtado
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  4. Stefan Langerman
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  5. Henk Meijer
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  6. Suneeta Ramaswami
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  7. Diane Souvaine
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  8. Godfried Toussaint
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Corresponding author

Correspondence to Godfried Toussaint.

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Colannino, J., Damian, M., Hurtado, F. et al. Efficient Many-To-Many Point Matching in One Dimension. Graphs and Combinatorics 23 (Suppl 1), 169–178 (2007). https://doi.org/10.1007/s00373-007-0714-3

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  • DOI: https://doi.org/10.1007/s00373-007-0714-3

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