### Abstract

Let A and B be two sets of n objects in R^{d}. We propose to use bottleneck matching as a convenient way for measuring the resemblance between them, and present several algorithms for computing, as well as approximating, this resemblance. The running time of all these algorithms is close to O(n^{1.5}). For instance, if the objects are points in the plane, the running time is O(n^{1.5} log n). We also consider the problem of finding a translation of B that maximizes the resemblance to A under the bottleneck matching criterion. When A and B are point-sets in the plane, we present an O(n^{5} log n) time algorithm for determining whether for some translated copy the resemblance gets below a given ρ, improving the previous result of Alt, Mehlhorn, Wagener and Welzl by a factor of almost n. We use this result to compute the smallest such ρ in time O(n^{5} log^{2} n), and give an efficient approximation scheme for this problem.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Publisher | ACM |

Pages | 301-310 |

Number of pages | 10 |

State | Published - 1996 |

Externally published | Yes |

Event | Proceedings of the 1996 12th Annual Symposium on Computational Geometry - Philadelphia, PA, USA Duration: May 24 1996 → May 26 1996 |

### Other

Other | Proceedings of the 1996 12th Annual Symposium on Computational Geometry |
---|---|

City | Philadelphia, PA, USA |

Period | 5/24/96 → 5/26/96 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Geometry and Topology

### Cite this

*Proceedings of the Annual Symposium on Computational Geometry*(pp. 301-310). ACM.

**Improvements on bottleneck matching and related problems using geometry.** / Efrat, Alon; Itai, Alon.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual Symposium on Computational Geometry.*ACM, pp. 301-310, Proceedings of the 1996 12th Annual Symposium on Computational Geometry, Philadelphia, PA, USA, 5/24/96.

}

TY - GEN

T1 - Improvements on bottleneck matching and related problems using geometry

AU - Efrat, Alon

AU - Itai, Alon

PY - 1996

Y1 - 1996

N2 - Let A and B be two sets of n objects in Rd. We propose to use bottleneck matching as a convenient way for measuring the resemblance between them, and present several algorithms for computing, as well as approximating, this resemblance. The running time of all these algorithms is close to O(n1.5). For instance, if the objects are points in the plane, the running time is O(n1.5 log n). We also consider the problem of finding a translation of B that maximizes the resemblance to A under the bottleneck matching criterion. When A and B are point-sets in the plane, we present an O(n5 log n) time algorithm for determining whether for some translated copy the resemblance gets below a given ρ, improving the previous result of Alt, Mehlhorn, Wagener and Welzl by a factor of almost n. We use this result to compute the smallest such ρ in time O(n5 log2 n), and give an efficient approximation scheme for this problem.

AB - Let A and B be two sets of n objects in Rd. We propose to use bottleneck matching as a convenient way for measuring the resemblance between them, and present several algorithms for computing, as well as approximating, this resemblance. The running time of all these algorithms is close to O(n1.5). For instance, if the objects are points in the plane, the running time is O(n1.5 log n). We also consider the problem of finding a translation of B that maximizes the resemblance to A under the bottleneck matching criterion. When A and B are point-sets in the plane, we present an O(n5 log n) time algorithm for determining whether for some translated copy the resemblance gets below a given ρ, improving the previous result of Alt, Mehlhorn, Wagener and Welzl by a factor of almost n. We use this result to compute the smallest such ρ in time O(n5 log2 n), and give an efficient approximation scheme for this problem.

UR - http://www.scopus.com/inward/record.url?scp=0029715023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029715023&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0029715023

SP - 301

EP - 310

BT - Proceedings of the Annual Symposium on Computational Geometry

PB - ACM

ER -