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 …

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 (∃R). A problem is\ensuremath ∃\mathbbR-complete if it is as hard as the …

In the Minimum Convex Cover (MCC) problem, we are given a simple polygon P and an
integer k, and the question is if there exist k convex polygons whose union is P. It is known …

We investigate the computational complexity of computing the Hausdorff distance.
Specifically, we show that the decision problem of whether the Hausdorff distance of two …

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 …

A continuous constraint satisfaction problem (CCSP) is a constraint satisfaction problem
(CSP) with the real numbers as domain. We engage in a systematic study to classify CCSPs …

We survey the complexity class $\exists\mathbb {R} $, which captures the complexity of
deciding the existential theory of the reals. The class $\exists\mathbb {R} $ has roots in two …

We show that the decision problem of determining whether a given (abstract simplicial)-
complex has a geometric embedding in is complete for the Existential Theory of the Reals …

We study the problem of finding an exact solution to the Consensus Halving problem. While
recent work has shown that the approximate version of this problem is PPA-complete …