Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Four results on randomized incremental constructions
Computational Geometry: Theory and Applications
Sign determination in residue number systems
Theoretical Computer Science - Special issue on real numbers and computers
Fast deterministic computation of determinants of dense matrices
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Computational Discrete Mathematics
A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
Dynamic Transitive Closure via Dynamic Matrix Inverse (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On the complexity of computing determinants
Computational Complexity
Incremental construction of the delaunay triangulation and the delaunay graph in medium dimension
Proceedings of the twenty-fifth annual symposium on Computational geometry
A simple division-free algorithm for computing determinants
Information Processing Letters
An output-sensitive algorithm for computing projections of resultant polytopes
Proceedings of the twenty-eighth annual symposium on Computational geometry
| Hi-index | 0.00 |
Determinant computation is the core procedure in many important geometric algorithms, such as convex hull computations and point locations. As the dimension of the computation space grows, a higher percentage of the computation time is consumed by these predicates. In this paper we study the sequences of determinants that appear in geometric algorithms. We use dynamic determinant algorithms to speed-up the computation of each predicate by using information from previously computed predicates. We propose two dynamic determinant algorithms with quadratic complexity when employed in convex hull computations, and with linear complexity when used in point location problems. Moreover, we implement them and perform an experimental analysis. Our implementations outperform the state-of-the-art determinant and convex hull implementations in most of the tested scenarios, as well as giving a speed-up of 78 times in point location problems.