计算几何

In this article, we consider the problems of finding in $d+1$ dimensions a minimum-volume axis-parallel box, a minimum-volume arbitrarily-oriented box and a minimum-volume convex body into which a given set of $d$-dimensional unit-radius…

We present a novel 2D convex hull peeling algorithm for outlier detection, which repeatedly removes the point on the hull that decreases the hull's area the most. To find k outliers among n points, one simply peels k points. The algorithm…

This paper introduces a novel computational framework for modeling and analyzing the spatiotemporal shape variability of tree-like 4D structures whose shapes deform and evolve over time. Tree-like 3D objects, such as botanical trees and…

In the paper ``Lower bounds on the number of crossing-free subgraphs of $K_N$'' (Computational Geometry 16 (2000), 211-221), it is shown that a double chain of $n$ points in the plane admits at least $\Omega(4.642126305^n)$ polygonizations,…

We propose a novel graph visualization method leveraging random walk-based embeddings to replace costly graph-theoretical distance computations. Using word2vec-inspired embeddings, our approach captures both structural and semantic…

In this paper, we introduce the following new concept in graph drawing. Our task is to find a small collection of drawings such that they all together satisfy some property that is useful for graph visualization. We propose investigating a…

We revisit the maximum range sum (MaxRS) problem: given a set $P$ of $n$ weighted points in $\mathbb{R}^d$ and a range $Q$ (typically axis-aligned $d$-box or $d$-ball), the goal is to place $Q$ to maximize the total weight of points in…

Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…

The presence of obstacles has a major impact on distance computation, motion planning, and visibility. While these problems are well studied in the plane, our understanding in three and higher dimensions is still limited. We investigate how…

In the Minimum Consistent Subset (MCS) problem, we are presented with a connected simple undirected graph $G=(V,E)$, consisting of a vertex set $V$ of size $n$ and an edge set $E$. Each vertex in $V$ is assigned a color from the set…

Train timetables can be represented as event graphs, where correspond to a train passing through a location at a certain point in time. A visual representation of an event graph is important for many applications such as dispatching and…

We explore an Art Gallery variant where each point of a polygon must be seen by k guards, and guards cannot see through other guards. Surprisingly, even covering convex polygons under this variant is not straightforward. For example,…

We initiate the study of computing shortest non-separating simple closed curves with some given topological properties on non-orientable surfaces. While, for orientable surfaces, any two non-separating simple closed curves are related by a…

Let $S$ be a set of $n$ points in the Euclidean plane and general position i.e., no three points are collinear. An \emph{at most $k$-out polygon of $S$} is a simple polygon such that each vertex is a point in $S$ and there are at most $k$…

We study the problem of partitioning a polygon into the minimum number of subpolygons using cuts in predetermined directions such that each resulting subpolygon satisfies a given width constraint. A polygon satisfies the unit-width…

The sliding square model is a widely used abstraction for studying self-reconfigurable robotic systems, where modules are square-shaped robots that move by sliding or rotating over one another. In this paper, we propose a novel distributed…

In the classic polyline simplification problem we want to replace a given polygonal curve $P$, consisting of $n$ vertices, by a subsequence $P'$ of $k$ vertices from $P$ such that the polygonal curves $P$ and $P'$ are as close as possible.…

Computing offsets of curves on parametric surfaces is a fundamental yet challenging operation in computer aided design and manufacturing. Traditional analytical approaches suffer from time-consuming geodesic distance queries and complex…

Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…

In neuroimaging, extensive post-processing of resting-state functional MRI (rfMRI) data is necessary for its application and investigation in relation to brain-behavior associations. Such post-processing is used to derive brain…