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COMPGEOM
2010
ACM
9 years 8 months ago
Tangencies between families of disjoint regions in the plane
Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the memb...
János Pach, Andrew Suk, Miroslav Treml
COMPGEOM
2010
ACM
9 years 8 months ago
Linkless and flat embeddings in 3-space and the unknot problem
Ken-ichi Kawarabayashi, Stephan Kreutzer, Bojan Mo...
COMPGEOM
2010
ACM
9 years 9 months ago
Manifold reconstruction using tangential Delaunay complexes
We give a provably correct algorithm to reconstruct a kdimensional manifold embedded in d-dimensional Euclidean space. Input to our algorithm is a point sample coming from an unkn...
Jean-Daniel Boissonnat, Arijit Ghosh
COMPGEOM
2010
ACM
9 years 9 months ago
The complexity of the normal surface solution space
Normal surface theory is a central tool in algorithmic threedimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important a...
Benjamin A. Burton
COMPGEOM
2010
ACM
9 years 10 months ago
Computing similarity between piecewise-linear functions
We study the problem of computing the similarity between two piecewise-linear bivariate functions defined over a common domain, where the surfaces they define in 3D—polyhedral...
Pankaj K. Agarwal, Boris Aronov, Marc J. van Kreve...
COMPGEOM
2010
ACM
9 years 10 months ago
A dynamic data structure for approximate range searching
In this paper, we introduce a simple, randomized dynamic data structure for storing multidimensional point sets, called a quadtreap. This data structure is a randomized, balanced ...
David M. Mount, Eunhui Park
COMPGEOM
2010
ACM
9 years 10 months ago
The 2-center problem in three dimensions
Let P be a set of n points in R3 . The 2-center problem for P is to find two congruent balls of the minimum radius whose union covers P. We present two randomized algorithms for ...
Pankaj K. Agarwal, Rinat Ben Avraham, Micha Sharir
COMPGEOM
2010
ACM
9 years 10 months ago
Optimal reconstruction might be hard
Sampling conditions for recovering the homology of a set using topological persistence are much weaker than sampling conditions required by any known algorithm for producing a top...
Dominique Attali, André Lieutier
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