### Abstract

Given n points in the plane and an integer k, the problem of selecting that pair of points that determines the line with the kth smallest or largest slope is considered. In the restricted case, where k is O(n), line sweeping gives an optimal, O(n log n)-time algorithm. For general k the parametric search technique of Megiddo is used to describe an O(n(log n)^{2})-time algorithm. This is modified to produce a new, optimal O(n log n)-time selection algorithm by incorporating an approximation idea.

Original language | English (US) |
---|---|

Pages (from-to) | 792-810 |

Number of pages | 19 |

Journal | SIAM Journal on Computing |

Volume | 18 |

Issue number | 4 |

State | Published - Aug 1989 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Theoretical Computer Science

### Cite this

*SIAM Journal on Computing*,

*18*(4), 792-810.

**Optimal-time algorithm for slope selection.** / Cole, Richard; Salowe, Jeffrey S.; Steiger, W. L.; Szemeredi, Endre.

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 18, no. 4, pp. 792-810.

}

TY - JOUR

T1 - Optimal-time algorithm for slope selection

AU - Cole, Richard

AU - Salowe, Jeffrey S.

AU - Steiger, W. L.

AU - Szemeredi, Endre

PY - 1989/8

Y1 - 1989/8

N2 - Given n points in the plane and an integer k, the problem of selecting that pair of points that determines the line with the kth smallest or largest slope is considered. In the restricted case, where k is O(n), line sweeping gives an optimal, O(n log n)-time algorithm. For general k the parametric search technique of Megiddo is used to describe an O(n(log n)2)-time algorithm. This is modified to produce a new, optimal O(n log n)-time selection algorithm by incorporating an approximation idea.

AB - Given n points in the plane and an integer k, the problem of selecting that pair of points that determines the line with the kth smallest or largest slope is considered. In the restricted case, where k is O(n), line sweeping gives an optimal, O(n log n)-time algorithm. For general k the parametric search technique of Megiddo is used to describe an O(n(log n)2)-time algorithm. This is modified to produce a new, optimal O(n log n)-time selection algorithm by incorporating an approximation idea.

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UR - http://www.scopus.com/inward/citedby.url?scp=0024716010&partnerID=8YFLogxK

M3 - Article

VL - 18

SP - 792

EP - 810

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 4

ER -