Given a simple polygon P, we say that two points p, q∈ P see each other if the line segment
pq is contained in P. A set of points G⊆ P is said to guard the polygon P if every point p∈ P …

The crossing number is a popular tool in graph drawing and visualization, but there is not
really just one crossing number; there is a large family of crossing number notions of which …

We consider the algorithmic problem of finding the optimal weights and biases for a two-
layer fully connected neural network to fit a given set of data points, also known as empirical …

We introduce the complexity class∃ ℝ ∃R based on the existential theory of the reals. We
show that the definition of∃ ℝ ∃R is robust in the sense that even the fragment of the theory …

In this survey/introductory article, we first present the basics of the field of Parameterized
Complexity, made accessible to readers without background on the subject. Afterwards, we …

Crossing Numbers of Graphs is the first book devoted to the crossing number, an
increasingly popular object of study with surprising connections. The field has matured into a …

Given a neural network, training data, and a threshold, finding weights for the neural network
such that the total error is below the threshold is known to be NP-hard. We determine the …

We study algorithmic problems that belong to the complexity class of the existential theory of
the reals (). A problem is-complete if it is as hard as the problem existential theory of the …

A graph G is a k-sphere graph if there are k-dimensional real vectors v1,..., vn such that ij∈
E (G) if and only if the distance between vi and vj is at most 1. A graph G is a k-dot product …

The aim in packing problems is to decide if a given set of pieces can be placed inside a
given container. A packing problem is defined by the types of pieces and containers to be …