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Stefan Schirra

Publications and source records attributed to Stefan Schirra.

7 recordsLinked to original sources
arXiv2026

Central Triangulation under Parallel Flip Operations: The CG:SHOP Challenge 2026

We give an overview of the 2026 Computational Geometry Challenge targeting the problem of finding a Central Triangulation under Parallel Flip Operations in triangulations of point sets. A flip is the parallel exchange of a set of edges in a triangulation with opposing diagonals of the convex quadrilaterals containing them. The challenge objective was, given a set of triangulations of a fixed point set, to determine a central triangulation with respect to parallel flip distances. More precisely, this asks for a triangulation that minimizes the sum of flip distances to all elements of the input

cs.CG↗
arXiv2025

Minimum Non-Obtuse Triangulations: The CG:SHOP Challenge 2025

We give an overview of the 2025 Computational Geometry Challenge targeting the problem Minimum Non-Obtuse Triangulation: Given a planar straight-line graph G in the plane, defined by a set of points in the plane (representing vertices) and a set of non-crossing line segments connecting them (representing edges); the objective is to find a feasible non-obtuse triangulation that uses a minimum number of Steiner points. If no triangulation without obtuse triangles is found, the secondary objective is to minimize the number of obtuse triangles in the triangulation.

cs.CG↗
arXiv2024

Maximum Polygon Packing: The CG:SHOP Challenge 2024

We give an overview of the 2024 Computational Geometry Challenge targeting the problem \textsc{Maximum Polygon Packing}: Given a convex region $P$ in the plane, and a collection of simple polygons $Q_1, \ldots, Q_n$, each $Q_i$ with a respective value $c_i$, find a subset $S \subseteq \{1, \ldots,n\}$ and a feasible packing within $P$ of the polygons $Q_i$ (without rotation) for $i \in S$, maximizing $\sum_{i \in S} c_i$. Geometric packing problems, such as this, present significant computational challenges and are of substantial practical importance.

cs.CG↗
arXiv2023

Minimum Coverage by Convex Polygons: The CG:SHOP Challenge 2023

We give an overview of the 2023 Computational Geometry Challenge targeting the problem Minimum Coverage by Convex Polygons, which consists of covering a given polygonal region (possibly with holes) by a minimum number of convex subsets, a problem with a long-standing tradition in Computational Geometry.

cs.CG↗
arXiv2017

Minimizing the Continuous Diameter when Augmenting a Geometric Tree with a Shortcut

We augment a tree $T$ with a shortcut $pq$ to minimize the largest distance between any two points along the resulting augmented tree $T+pq$. We study this problem in a continuous and geometric setting where $T$ is a geometric tree in the Euclidean plane, where a shortcut is a line segment connecting any two points along the edges of $T$, and we consider all points on $T+pq$ (i.e., vertices and points along edges) when determining the largest distance along $T+pq$. We refer to the largest distance between any two points along edges as the continuous diameter to distinguish it from the discrete diameter, i.e., the largest distance between any two vertices. We establish that a single shortcut is sufficient to reduce the continuous diameter of a geometric tree $T$ if and only if the intersection of all diametral paths of $T$ is neither a line segment nor a single point. We determine an optimal shortcut for a geometric tree with $n$ straight-line edges in $O(n \log n)$ time. Apart from the running time, our results extend to geometric trees whose edges are rectifiable curves. The algorithm for trees generalizes our algorithm for paths.

cs.CG↗
arXiv2013

Network Farthest-Point Diagrams

Consider the continuum of points along the edges of a network, i.e., an undirected graph with positive edge weights. We measure distance between these points in terms of the shortest path distance along the network, known as the network distance. Within this metric space, we study farthest points. We introduce network farthest-point diagrams, which capture how the farthest points---and the distance to them---change as we traverse the network. We preprocess a network G such that, when given a query point q on G, we can quickly determine the farthest point(s) from q in G as well as the farthest distance from q in G. Furthermore, we introduce a data structure supporting queries for the parts of the network that are farther away from q than some threshold R > 0, where R is part of the query. We also introduce the minimum eccentricity feed-link problem defined as follows. Given a network G with geometric edge weights and a point p that is not on G, connect p to a point q on G with a straight line segment pq, called a feed-link, such that the largest network distance from p to any point in the resulting network is minimized. We solve the minimum eccentricity feed-link problem using eccentricity diagrams. In addition, we provide a data structure for the query version, where the network G is fixed and a query consists of the point p.

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