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Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2012

Matching solid shapes in arbitrary dimension via random sampling

Résumé

We give simple probabilistic algorithms that approximately maximize the volume of overlap of two solid, i.e. full-dimensional, shapes under translations and rigid motions. The shapes are subsets of $ℝ^d$ where $d≥ 2$. The algorithms approximate with respect to an pre-specified additive error and succeed with high probability. Apart from measurability assumptions, we only require that points from the shapes can be generated uniformly at random. An important example are shapes given as finite unions of simplices that have pairwise disjoint interiors.
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Dates et versions

hal-01197244 , version 1 (11-09-2015)

Identifiants

Citer

Daria Schymura. Matching solid shapes in arbitrary dimension via random sampling. 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'12), 2012, Montreal, Canada. pp.167-178, ⟨10.46298/dmtcs.2992⟩. ⟨hal-01197244⟩

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