Computing the extreme distances between two convex polygons
Journal of Algorithms
Computational geometry: an introduction
Computational geometry: an introduction
Complexity of fixed point computations
Complexity of fixed point computations
Approximation of Convex Polygons
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Determining the Separation of Preprocessed Polyhedra - A Unified Approach
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Approximation of Convex Figures by Pairs of Rectangles
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
A kinetic framework for computational geometry
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
A compact piecewise-linear Voronoi diagram for convex sites in the plane
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Optimizing Constrained Offset and Scaled Polygonal Annuli
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
A (1 + ɛ)-approximation algorithm for 2-line-center
Computational Geometry: Theory and Applications
Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets
Computational Geometry: Theory and Applications
Optimal simplification of polygonal chain for rendering
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Covering points with a polygon
Computational Geometry: Theory and Applications
Design and optimization of distributed sensing coverage in wireless sensor networks
ACM Transactions on Embedded Computing Systems (TECS)
Optimal simplification of polygonal chains for subpixel-accurate rendering
Computational Geometry: Theory and Applications
Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets
Computational Geometry: Theory and Applications
Computation of non-dominated points using compact voronoi diagrams
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
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Motivated by problems in computational geometry, this paper investigates the complexity of finding a fixed-point of the composition of two or three continuous functions that are defined piecewise. It shows that certain cases require nested binary search taking Θ(log2 n) time. Other cases can be solved in logarithmic time by using a prune-and-search technique that may make tentative discards and later revoke or certify them. This work finds application in optimal subroutines that compute approximations to convex polygons, dense packings, and Voronoi vertices for Euclidean and polygonal distance functions.