Related papers: A Rank-based Convex Hull method for Dense Data Set…
For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that is, the…
We describe an algorithm for computing the convex hull of a finite collection of points in the affine building of SL_d(K), for K a field with discrete valuation. These convex hulls describe the relations among a finite collection of…
For a planar point set $P$, its convex hull is the smallest convex polygon that encloses all points in $P$. The construction of the convex hull from an array $I_P$ containing $P$ is a fundamental problem in computational geometry. By…
This paper describes a novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run time needed to find the maximum distance of two points in E2. It can be easily modified for the E3 case in…
Inspired by the classical fractional cascading technique, we introduce new techniques to speed up the following type of iterated search in 3D: The input is a graph $\mathbf{G}$ with bounded degree together with a set $H_v$ of 3D hyperplanes…
Finding a good classifier is a multiobjective optimization problem with different error rates and the costs to be minimized. The receiver operating characteristic is widely used in the machine learning community to analyze the performance…
Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An…
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…
We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict…
The retrieval problem is the problem of associating data with keys in a set. Formally, the data structure must store a function f: U ->{0,1}^r that has specified values on the elements of a given set S, a subset of U, |S|=n, but may have…
A new approach to the local and global explanation is proposed. It is based on selecting a convex hull constructed for the finite number of points around an explained instance. The convex hull allows us to consider a dual representation of…
We propose an algorithm for clustering high dimensional data. If $P$ features for $N$ objects are represented in an $N\times P$ matrix ${\bf X}$, where $N\ll P$, the method is based on exploiting the cluster-dependent structure of the…
We study $\mathbb{R}^2\oplus\mathbb{R}$-separately convex hulls of finite sets of points in $\mathbb{R}^3$, as in KirchheimMullerSverak2003. This notion of convexity, which we call $2+1$ convexity, corresponds to rank-one convex convexity,…
Geodesic shooting has been successfully applied to diffeo-morphic registration of point sets. Exact computation of the geodesicshooting between point sets, however, requiresO(N2) calculations each time step on the number of points in the…
The computation of determinants or their signs is the core procedure in many important geometric algorithms, such as convex hull, volume and point location. As the dimension of the computation space grows, a higher percentage of the total…
A convex partition of a point set P in the plane is a planar partition of the convex hull of P with empty convex polygons or internal faces whose extreme points belong to P. In a convex partition, the union of the internal faces give the…
Refinements of the worst case complexity over instances of fixed input size consider the input order or the input structure, but rarely both at the same time. Barbay et al. [2016] described ``synergistic'' solutions on multisets, which take…
In the convex covering problem, we are given a convex polygon with holes $P$ and the goal is to cover $P$ using a small number of convex polygons that lie inside $P$. In this paper, we solve the problem using the following strategy. We find…
Efficient extraction of useful knowledge from these data is still a challenge, mainly when the data is distributed, heterogeneous and of different quality depending on its corresponding local infrastructure. To reduce the overhead cost,…
This paper argues that DNNs implement a computational Occam's razor -- finding the `simplest' algorithm that fits the data -- and that this could explain their incredible and wide-ranging success over more traditional statistical methods.…