Nearest-neighbor searching under uncertainty II

PK Agarwal, B Aronov, S Har-Peled… - ACM Transactions on …, 2016‏ - dl.acm.org
Nearest-neighbor search, which returns the nearest neighbor of a query point in a set of
points, is an important and widely studied problem in many fields, and it has a wide range of …

Delaunay triangulations of imprecise pointsin linear time after preprocessing

M Löffler, J Snoeyink - Proceedings of the twenty-fourth annual …, 2008‏ - dl.acm.org
An assumption of nearly all algorithms in computational geometry is that the input points are
given precisely, so it is interesting to ask what is the value of imprecise information about …

Delaunay triangulations in O(sort(n)) time and more

K Buchin, W Mulzer - Journal of the ACM (JACM), 2011‏ - dl.acm.org
We present several results about Delaunay triangulations (DTs) and convex hulls in
transdichotomous and hereditary settings:(i) the DT of a planar point set can be computed in …

[HTML][HTML] Computing the Fréchet distance between uncertain curves in one dimension

K Buchin, M Löffler, T Ophelders, A Popov… - Computational …, 2023‏ - Elsevier
We consider the problem of computing the Fréchet distance between two curves for which
the exact locations of the vertices are unknown. Each vertex may be placed in a given …

[HTML][HTML] Closest pair and the post office problem for stochastic points

P Kamousi, TM Chan, S Suri - Computational Geometry, 2014‏ - Elsevier
Given a (master) set M of n points in d-dimensional Euclidean space, consider drawing a
random subset that includes each point mi∈ M with an independent probability p i. How …

Preprocessing imprecise points for Delaunay triangulation: Simplified and extended

K Buchin, M Löffler, P Morin, W Mulzer - Algorithmica, 2011‏ - Springer
Suppose we want to compute the Delaunay triangulation of a set P whose points are
restricted to a collection ℛ of input regions known in advance. Building on recent work by …

Fréchet distance for uncertain curves

K Buchin, C Fan, M Löffler, A Popov, B Raichel… - ACM Transactions on …, 2023‏ - dl.acm.org
In this article, we study a wide range of variants for computing the (discrete and continuous)
Fréchet distance between uncertain curves. An uncertain curve is a sequence of uncertainty …

Unions of onions: Preprocessing imprecise points for fast onion decomposition

M Löffler, W Mulzer - arxiv preprint arxiv:1302.5328, 2013‏ - arxiv.org
Let $\mathcal {D} $ be a set of $ n $ pairwise disjoint unit disks in the plane. We describe
how to build a data structure for $\mathcal {D} $ so that for any point set $ P $ containing …

Preprocessing ambiguous imprecise points

I Van Der Hoog, I Kostitsyna, M Löffler… - arxiv preprint arxiv …, 2019‏ - arxiv.org
Let ${R}=\{R_1, R_2,..., R_n\} $ be a set of regions and let $ X=\{x_1, x_2,..., x_n\} $ be an
(unknown) point set with $ x_i\in R_i $. Region $ R_i $ represents the uncertainty region of …

Computing hereditary convex structures

B Chazelle, W Mulzer - Proceedings of the twenty-fifth annual …, 2009‏ - dl.acm.org
Color red and blue the n vertices of a convex polytope P in R3. Can we compute the convex
hull of each color class in o (n log n)? What if we have k> 2 colors? What if the colors are …