## Abstract

Motivated by networks interplay, we study the problem of computing monochromatic plane matchings in bicolored point set. Given a bicolored set P of n red and m blue points in the plane, where n and m are even, the goal is to compute a plane matching M_{R} of the red points and a plane matching M_{B} of the blue points that minimize the number of crossing between M_{R} and M_{B} as well as the longest edge in M_{R} ∪ M_{B}. In this paper, we give asymptotically tight bound on the number of crossings between M_{R} and M_{B} when the points of P are in convex position. Moreover, we present an algorithm that computes bottleneck plane matchings M_{R} and M_{B}, such that there are no crossings between M_{R} and M_{B}, if such matchings exist. For points in general position, we present a polynomial-time approximation algorithm that computes two plane matchings with linear number of crossings between them.

Original language | English |
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Pages | 7-12 |

Number of pages | 6 |

State | Published - 1 Jan 2017 |

Event | 29th Canadian Conference on Computational Geometry, CCCG 2017 - Ottawa, Canada Duration: 26 Jul 2017 → 28 Jul 2017 |

### Conference

Conference | 29th Canadian Conference on Computational Geometry, CCCG 2017 |
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Country/Territory | Canada |

City | Ottawa |

Period | 26/07/17 → 28/07/17 |

## ASJC Scopus subject areas

- Computational Mathematics
- Geometry and Topology