Mikkel Abrahamsen | DeepAI

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∙ 03/01/2023

Coordination of Multiple Robots along Given Paths with Bounded Junction Complexity

We study a fundamental NP-hard motion coordination problem for multi-rob...

0 Mikkel Abrahamsen, et al. ∙

∙ 11/02/2022

Partitioning a Polygon Into Small Pieces

We study the problem of partitioning a given simple polygon P into a min...

0 Mikkel Abrahamsen, et al. ∙

∙ 08/15/2022

Degree of Convexity and Expected Distances in Polygons

We present an algorithm for computing the so-called Beer-index of a poly...

0 Mikkel Abrahamsen, et al. ∙

∙ 12/07/2021

Online Sorting and Translational Packing of Convex Polygons

We investigate various online packing problems in which convex polygons ...

0 Anders Aamand, et al. ∙

∙ 08/10/2021

Distinguishing classes of intersection graphs of homothets or similarities of two convex disks

For smooth convex disks A, i.e., convex compact subsets of the plane wit...

0 Mikkel Abrahamsen, et al. ∙

∙ 08/05/2021

Geometric Embeddability of Complexes is ∃ℝ-complete

We show that the decision problem of determining whether a given (abstra...

0 Mikkel Abrahamsen, et al. ∙

∙ 06/04/2021

Covering Polygons is Even Harder

In the MINIMUM CONVEX COVER (MCC) problem, we are given a simple polygon...

0 Mikkel Abrahamsen, et al. ∙

∙ 03/17/2021

Chasing Puppies: Mobile Beacon Routing on Closed Curves

We solve an open problem posed by Michael Biro at CCCG 2013 that was ins...

0 Mikkel Abrahamsen, et al. ∙

∙ 02/19/2021

Training Neural Networks is ER-complete

Given a neural network, training data, and a threshold, it was known tha...

0 Mikkel Abrahamsen, et al. ∙

∙ 01/22/2021

Online Packing to Minimize Area or Perimeter

We consider online packing problems where we get a stream of axis-parall...

0 Mikkel Abrahamsen, et al. ∙

∙ 12/21/2020

Escaping an Infinitude of Lions

We consider the following game played in the Euclidean plane: There is a...

0 Mikkel Abrahamsen, et al. ∙

∙ 11/22/2020

Tiling with Squares and Packing Dominos in Polynomial Time

We consider planar tiling and packing problems with polyomino pieces and...

0 Anders Aamand, et al. ∙

∙ 04/16/2020

Framework for ∃ℝ-Completeness of Two-Dimensional Packing Problems

We show that many natural two-dimensional packing problems are algorithm...

0 Mikkel Abrahamsen, et al. ∙

∙ 12/18/2019

Dynamic Toolbox for ETRINV

Recently, various natural algorithmic problems have been shown to be ∃R-...

0 Mikkel Abrahamsen, et al. ∙

∙ 09/02/2019

Disks in Curves of Bounded Convex Curvature

We say that a simple, closed curve γ in the plane has bounded convex cur...

0 Anders Aamand, et al. ∙

∙ 02/11/2019

Geometric Multicut

We study the following separation problem: Given a collection of colored...

0 Mikkel Abrahamsen, et al. ∙

∙ 02/05/2019

Classifying Convex Bodies by their Contact and Intersection Graphs

Suppose that A is a convex body in the plane and that A_1,...,A_n are tr...

0 Anders Aamand, et al. ∙

∙ 03/31/2018

Fast Fencing

We consider very natural "fence enclosure" problems studied by Capoyleas...

0 Mikkel Abrahamsen, et al. ∙

∙ 05/17/2017

Range-Clustering Queries

In a geometric k-clustering problem the goal is to partition a set of po...

0 Mikkel Abrahamsen, et al. ∙

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