An optimal-time algorithm for slope selection

Given $n$ points in the plane and an integer $k$, the problem of selecting that pair of points that determines the line with the $k$th 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 $k$ th...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	SIAM journal on computing Ročník 18; číslo 4; s. 792 - 810
Hlavní autoři:	COLE, R, SALOWE, J. S, STEIGER, W. L, SZEMEREDI, E
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.08.1989
Témata:	Algorithms Applied mathematics Combinatorics Combinatorics. Ordered structures Computer science Decision trees Designs and configurations Exact sciences and technology Mathematics Sciences and techniques of general use Computational geometry Configuration Combinatorics Time complexity Algorithm analysis Optimization Slope
ISSN:	0097-5397, 1095-7111
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Popis
Shrnutí:	Given $n$ points in the plane and an integer $k$, the problem of selecting that pair of points that determines the line with the $k$th 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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14
ISSN:	0097-5397 1095-7111
DOI:	10.1137/0218055