Related papers: Computing skeletons for rectilinearly-convex obsta…
In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate…
Euclidean Steiner trees are relevant to model minimal networks in real-world applications ubiquitously. In this paper, we study the feasibility of a hierarchical approach embedded with bundling operations to compute multiple and mutually…
Deep Learning for Geometric Shape Understating has organized a challenge for extracting different kinds of skeletons from the images of different objects. This competition is organized in association with CVPR 2019. There are three…
Given a set of pairwise disjoint polygonal obstacles in the plane, finding an obstacle-avoiding Euclidean shortest path between two points is a classical problem in computational geometry and has been studied extensively. Previously,…
In this paper we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration and jerk constraints. Such a problem arises in industrial contexts such as automated…
The tree reconstruction problem is to find an embedded straight-line tree that approximates a given cloud of unorganized points in $\mathbb{R}^m$ up to a certain error. A practical solution to this problem will accelerate a discovery of new…
A drawing of a graph in the plane is {\it pseudolinear} if the edges of the drawing can be extended to doubly-infinite curves that form an arrangement of pseudolines, that is, any pair of edges crosses precisely once. A special case are…
This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is…
We consider the Minimum Steiner Cut problem on undirected planar graphs with non-negative edge weights. This problem involves finding the minimum cut of the graph that separates a specified subset $X$ of vertices (terminals) into two parts.…
The geometric intersection number of a curve on a surface is the minimal number of self-intersections of any homotopic curve, i.e. of any curve obtained by continuous deformation. Given a curve $c$ represented by a closed walk of length at…
When algorithmic skeletons were first introduced by Cole in late 1980 the idea had an almost immediate success. The skeletal approach has been proved to be effective when application algorithms can be expressed in terms of skeletons…
Motivated by the desire to cope with data imprecision, we study methods for taking advantage of preliminary information about point sets in order to speed up the computation of certain structures associated with them. In particular, we…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…
The next generation of aircraft collision avoidance systems frame the problem as a Markov decision process and use dynamic programming to optimize the alerting logic. The resulting system uses a large lookup table to determine advisories…
Given two points in the plane, a set of obstacles defined by closed curves, and an integer $k$, does there exist a path between the two designated points intersecting at most $k$ of the obstacles? This is a fundamental and well-studied…
Let $S$ and $D$ each be a set of orthogonal line segments in the plane. A line segment $s\in S$ \emph{stabs} a line segment $s'\in D$ if $s\cap s'\neq\emptyset$. It is known that the problem of stabbing the line segments in $D$ with the…
An \emph{obstacle representation} of a graph consists of a set of polygonal obstacles and a distinct point for each vertex such that two points see each other if and only if the corresponding vertices are adjacent. Obstacle representations…
Memetic Computing is a subject in computer science which considers complex structures as the combination of simple agents, memes, whose evolutionary interactions lead to intelligent structures capable of problem-solving. This paper focuses…
We consider the problem of cutting a set of edges on a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk, minimizing either the total number of cut edges or their total length. We show that this…
In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…