Related papers: On the Difficulty of Intersection Checking with Po…
We consider asymmetric convex intersection testing (ACIT). Let $P \subset \mathbb{R}^d$ be a set of $n$ points and $\mathcal{H}$ a set of $n$ halfspaces in $d$ dimensions. We denote by $\text{ch}(P)$ the polytope obtained by taking the…
The goal of this work is to develop a new universal high order subroutine for shock boundary layer interaction. First, an effective shock/discontinuity detector has been developed.The detector has two steps.The first step is to check the…
We study geometric variations of the discriminating code problem. In the \emph{discrete version} of the problem, a finite set of points $P$ and a finite set of objects $S$ are given in $\mathbb{R}^d$. The objective is to choose a subset…
In this paper, we address the risk estimation problem where one aims at estimating the probability of violation of safety constraints for a robot in the presence of bounded uncertainties with arbitrary probability distributions. In this…
State-of-the-art object pose estimation handles multiple instances in a test image by using multi-model formulations: detection as a first stage and then separately trained networks per object for 2D-3D geometric correspondence prediction…
In this paper the problem of maximizing the distance to a given fixed point over an intersection of balls is considered. It is known that this problem is NP complete in the general case, since any subset sum problem can be solved upon…
Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We relate this problem to a Voronoi-type diagram and derive…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
Abstract. The Set Intersection Problem (SIP) is the problem of finding a point in the intersection of convex sets. This problem is typically solved by the method of alternating projections. To accelerate the convergence, the idea of using…
The estimation of correspondences between two images resp. point sets is a core problem in computer vision. One way to formulate the problem is graph matching leading to the quadratic assignment problem which is NP-hard. Several so called…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure. These systems may be used to model higher-order programs and are closely related to the…
In this paper, we study the problem of minimizing a polynomial function with literals over all binary points, often referred to as pseudo-Boolean optimization. We investigate the fundamental limits of computation for this problem by…
Addressing pedestrian safety at intersections is one of the paramount concerns in the field of transportation research, driven by the urgency of reducing traffic-related injuries and fatalities. With advances in computer vision technologies…
A method is developed to calculate collision probability in this paper. Based on the encounter geometric features of space objects, it is reasonable to separate the radial orbital motions from that in the cross section for most encounter…
This research introduces two efficient methods to estimate the collision risk of planned trajectories in autonomous driving under uncertain driving conditions. Deterministic collision checks of planned trajectories are often inaccurate or…
Galois/monodromy groups attached to parametric systems of polynomial equations provide a method for detecting the existence of symmetries in solution sets. Beyond the question of existence, one would like to compute formulas for these…
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…
Deep Neural Networks (DNNs) have grown in popularity over the past decade and are now being used in safety-critical domains such as aircraft collision avoidance. This has motivated a large number of techniques for finding unsafe behavior in…