Tight time bounds for the minimum local convex partition problem

Authors:
Magdalene Grantson;Christos Levcopoulos
Affiliations:
Department of Computer Science, Lund University, Lund, Sweden;Department of Computer Science, Lund University, Lund, Sweden
Venue:
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Year:
2004

Citing 6
Cited 0

A heuristic triangulation algorithm

Journal of Algorithms
The boolean basis problem and how to cover some polygons by rectangles

SIAM Journal on Discrete Mathematics
Randomized complexity lower bounds

STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Lower bounds for algebraic computation trees

STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Algebraic computation trees in characteristic p0

SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Time bounds for selection

Journal of Computer and System Sciences

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let v be a vertex with n edges incident to it, such that the n edges partition an infinitesimally small circle C around v into convex pieces. The minimum local convex partition (MLCP) problem asks for two or three out of the n edges that still partition C into convex pieces and that are of minimum total length. We present an optimal algorithm solving the problem in linear time if the edges incident to v are sorted clockwise by angle. For unsorted edges our algorithm runs in O(n log n) time. For unsorted edges we also give a linear time approximation algorithm and a lower time bound.