Robust proximity queries: an illustration of degree-driven algorithm design
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Algebraic methods and arithmetic filtering for exact predicates on circle arcs
Proceedings of the sixteenth annual symposium on Computational geometry
Optimizing the sum of linear fractional functions and applications
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Improved construction of vertical decompositions of three-dimensional arrangements
Proceedings of the eighteenth annual symposium on Computational geometry
Reporting intersections among thick objects
Information Processing Letters
Root comparison techniques applied to computing the additively weighted Voronoi diagram
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal, Suboptimal, and Robust Algorithms for Proximity Graphs
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
PVD: A Stable Implementation for Computing Voronoi Diagrams of Polygonal Pockets
ALENEX '01 Revised Papers from the Third International Workshop on Algorithm Engineering and Experimentation
Upward Planarity Checking: ``Faces Are More than Polygons''
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Optimal and suboptimal robust algorithms for proximity graphs
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Robustness of k-gon Voronoi diagram construction
Information Processing Letters
The unpredictable deviousness of models
Theoretical Computer Science
Computing the Implicit Voronoi Diagram in Triple Precision
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Robustness of k-gon Voronoi diagram construction
Information Processing Letters
Proceedings of the twenty-sixth annual symposium on Computational geometry
Algorithms and theory of computation handbook
Can nearest neighbor searching be simple and always fast?
ESA'11 Proceedings of the 19th European conference on Algorithms
Algebraic methods and arithmetic filtering for exact predicates on circle arcs
Computational Geometry: Theory and Applications
Hi-index | 0.00 |
In the context of methodologies intended to confer robustness to geometric algorithms, we elaborate on the exact-computation paradigm and formalize the notion of degree of a geometric algorithm as a worst-case quantification of the precision (number of bits) to which arithmetic calculation have to be executed in order to guarantee topological correctness. We also propose a formalism for the expeditious evaluation of algorithmic degree. As an application of this paradigm and an illustration of our general approach where algorithm design is driven also by the degree, we consider the important classical problem of proximity queries in two and three dimensions and develop a new technique for the efficient and robust execution of such queries based on an implicit representation of Voronoi diagrams. Our new technique offers both low degree and fast query time and for 2D queries is optimal with respect to both cost measures of the paradigm, asymptotic number of operations, and arithmetic degree.