Abstract
This paper considers the situation where one is given a finite set of n points in the plane each of which is labeled either “positive” or “negative”. The problem is to find a bounded convex polygon of maximum area, the vertices of which are positive points and which does not contain any negative point. It is shown that this problem can be solved in time O(n 4 log n). Instead of using the area as the quantity to be maximized one may also use other measures fulfilling a certain additive property, e.g. the number of positive points contained in the polygon.
The author gratefully acknowledges the support of Deutsche Forschungsgemeinschaft grant 1066/6-1.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
A.Aggawal,S.Suri, Fast Algoritms for Computing the Largest Empty Rectangle, Proc. 3rd Symp. on Computational Geometry. p. 278–290, (1987).
B.Chazelle,R.L.Drysdale,D.T.Lee, Computing the Largest Empty Rectangle, SIAM J. Comput., vol 15, p. 300–315, (1986).
D.Eppstein,M.Overmars,G.Rote,G.Woeginger, Finding Minimum Area k-gons, Discrete Computational Geometry, vol 7,p. 45–58, (1992).
H.Edelsbrunner,F.P.Preparata, Minimal Polygonal Separation, Inf. Comput., vol 77,p. 218–232, (1988).
F.Preparata,M.Shamos, Computational Geometry, Springer Verlag, (1985).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fischer, P. (1993). Finding maximum convex polygons. In: Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 1993. Lecture Notes in Computer Science, vol 710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57163-9_19
Download citation
DOI: https://doi.org/10.1007/3-540-57163-9_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57163-6
Online ISBN: 978-3-540-47923-9
eBook Packages: Springer Book Archive