Related papers: Subsumption Algorithms for Three-Valued Geometric …
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
In this paper, we study two classic optimization problems: minimum geometric dominating set and set cover. In the dominating-set problem, for a given set of objects in {the} plane as input, the objective is to choose a minimum number of…
The local arrangement of atoms is one of the most important predictors of mechanical and functional properties of materials. However, algorithms for identifying the geometrical arrangements of atoms in complex materials systems are lacking.…
Image matching is a fundamental problem in Computer Vision with direct applications in robotics, remote sensing, and geospatial data analysis. We present an analytical and experimental evaluation of classical local feature-based image…
Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes…
Mutual coherence is a measure of similarity between two opinions. Although the notion comes from philosophy, it is essential for a wide range of technologies, e.g., the Wahl-O-Mat system. In Germany, this system helps voters to find…
Defeaturing consists in simplifying geometrical models by removing the geometrical features that are considered not relevant for a given simulation. Feature removal and simplification of computer-aided design models enables faster…
The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If…
It is well known that popular optimization techniques can lead to overfitting or even a lack of convergence altogether; thus, practitioners often utilize ad hoc regularization terms added to the energy functional. When carefully crafted,…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…
Geometric programming problems occur frequently in engineering design and management. In multiobjective optimization, the trade-off information between different objective functions is probably the most important piece of information in a…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
This paper describes a simpler way for programmers to reason about the correctness of their code. The study of semantics of logic programs has shown strong links between the model theoretic semantics (truth and falsity of atoms in the…
We consider the problem of translating between irreducible closed sets and implicational bases in closure systems. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph…