### 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(n ^{2}) for the same problem.

Original language | English (US) |
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Pages (from-to) | 169-178 |

Number of pages | 10 |

Journal | Graphs and Combinatorics |

Volume | 23 |

Issue number | SUPPL. 1 |

DOIs | |

State | Published - Jun 1 2007 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Cite this

*Graphs and Combinatorics*,

*23*(SUPPL. 1), 169-178. https://doi.org/10.1007/s00373-007-0714-3