Related papers: Geodesic-Preserving Polygon Simplification

The geodesic between two points $a$ and $b$ in the interior of a simple polygon~$P$ is the shortest polygonal path inside $P$ that connects $a$ to $b$. It is thus the natural generalization of straight line segments on unconstrained point…

Detecting polygons defined by a set of line segments in a plane is an important step in analyzing vector drawings. This paper presents an approach combining several algorithms to detect basic polygons from arbitrary line segments. The…

We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…

We study the problem of decomposing (i.e. partitioning and covering) polygons into components that are $\alpha$-fat, which means that the aspect ratio of each subpolygon is at most $\alpha$. We consider decompositions without Steiner…

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.…

In this paper, we have examined the problem of embedding a cycle of n vertices onto a given set of n points inside a simple polygon. The goal of the problem is that the cycle must be embedded without bends and does not intersect itself and…

Geometric embedding of graphs in a point set in the plane is a well known problem. In this paper, the complexity of a variant of this problem, where the point set is bounded by a simple polygon, is considered. Given a point set in the plane…

Geometric shape classification of vector polygons remains a challenging task in spatial analysis. Previous studies have primarily focused on deep learning approaches for rasterized vector polygons, while the study of discrete polygon…

A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…

Acceleration of algorithms is becoming a crucial problem, if larger data sets are to be processed. Evaluation of algorithms is mostly done by using computational geometry approach and evaluation of computational complexity. However in…

In the discrete Tempotron learning problem a neuron receives time varying inputs and for a set of such input sequences ($\mathcal S_-$ set) the neuron must be sub-threshold for all times while for some other sequences ($\mathcal S_+$ set)…

Let $\mathcal{P}$ be a simple polygon with $m$ vertices and let $P$ be a set of $n$ points inside $\mathcal{P}$. We prove that there exists, for any $\varepsilon>0$, a set $\mathcal{C} \subset P$ of size $O(1/\varepsilon^2)$ such that the…

We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

For an optimization problem $\Pi$ on graphs whose solutions are vertex sets, a vertex $v$ is called $c$-essential for $\Pi$ if all solutions of size at most $c \cdot OPT$ contain $v$. Recent work showed that polynomial-time algorithms to…

Let $s$ be a source point and $t$ be a destination point inside an $n$-vertex simple polygon $P$. Euclidean shortest paths and minimum-link paths between $s$ and $t$ inside $P$ have been well studied. Both these kinds of paths are simple…

We are given a read-only memory for input and a write-only stream for output. For a positive integer parameter s, an s-workspace algorithm is an algorithm using only $O(s)$ words of workspace in addition to the memory for input. In this…

In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…

This paper presents a geometric approach to the classical isoperimetric problem by analysing the efficiency of regular polygons in enclosing maximum area for a fixed perimeter. Using efficiency metrics, it proves that regular polygons…

In this paper we show how to combine two algorithmic techniques to obtain linear time algorithms for various optimization problems on graphs, and present a subroutine which will be useful in doing so. The first technique is iterative…