Computational geometry: an introduction
Computational geometry: an introduction
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
On the computational complexity of approximating solutions for real algebraic formulae
SIAM Journal on Computing
On the area of overlap of translated polygons
Computer Vision and Image Understanding
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
On some geometric optimization problems in layered manufacturing
Computational Geometry: Theory and Applications
Computing the arrangement of curve segments: divide-and-conquer algorithms via sampling
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
Efficient algorithms for shared camera control
Proceedings of the nineteenth annual symposium on Computational geometry
Almost tight upper bounds for vertical decompositions in four dimensions
Journal of the ACM (JACM)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Maximizing the overlap of two planar convex sets under rigid motions
Computational Geometry: Theory and Applications
How to get close to the median shape
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
Finding a Guard that Sees Most and a Shop that Sells Most
Discrete & Computational Geometry
On Overlays and Minimization Diagrams
Discrete & Computational Geometry
Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets
Computational Geometry: Theory and Applications
A near-linear algorithm for projective clustering integer points
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A generalization of the convex kakeya problem
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Optimization schemes for protective jamming
Proceedings of the thirteenth ACM international symposium on Mobile Ad Hoc Networking and Computing
Maximum overlap of convex polytopes under translation
Computational Geometry: Theory and Applications
Shape matching under rigid motion
Computational Geometry: Theory and Applications
Overlap of convex polytopes under rigid motion
Computational Geometry: Theory and Applications
Optimization Schemes for Protective Jamming
Mobile Networks and Applications
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We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of non-negative, constant description-complexity algebraic functions. We first give a FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions, and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum area hulls.