6 papers
Gap-ETH-Tight Approximation Schemes for Red-Green-Blue Separation and Bicolored Noncrossing Euclidean Travelling Salesman Tours
François Dross, Krzysztof Fleszar, Karol Węgrzycki +1
In this paper, we study problems of connecting classes of points via noncrossing structures. Given a set of colored terminal points, we want to find a graph for each color that con…
Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity
Timothy M. Chan, Thomas C. van Dijk, Krzysztof Fleszar +2
We initiate the study of the following natural geometric optimization problem. The input is a set of axis-aligned rectangles in the plane. The objective is to find a set of horizon…
A PTAS for Euclidean TSP with Hyperplane Neighborhoods
Antonios Antoniadis, Krzysztof Fleszar, Ruben Hoeksma +1
In the Traveling Salesperson Problem with Neighborhoods (TSPN), we are given a collection of geometric regions in some space. The goal is to output a tour of minimum length that vi…
The Complexity of Drawing Graphs on Few Lines and Few Planes
Steven Chaplick, Krzysztof Fleszar, Fabian Lipp +3
It is well known that any graph admits a crossing-free straight-line drawing in and that any planar graph admits the same even in . For a graph and…
Minimum Rectilinear Polygons for Given Angle Sequences
William S. Evans, Krzysztof Fleszar, Philipp Kindermann +3
A rectilinear polygon is a polygon whose edges are axis-aligned. Walking counterclockwise on the boundary of such a polygon yields a sequence of left turns and right turns. The num…
New Algorithms for Maximum Disjoint Paths Based on Tree-Likeness
Krzysztof Fleszar, Matthias Mnich, Joachim Spoerhase
We study the classical NP-hard problems of finding maximum-size subsets from given sets of terminal pairs that can be routed via edge-disjoint paths (MaxEDP) or node-disjoint p…