相关论文: Computational Geometry Column 35

Path finding algorithm addresses problem of finding shortest path from source to destination avoiding obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike most path finding algorithms…

A high-level description of an algorithm which computes the minimum perimeter triangle enclosing a convex polygon in linear time exists in the literature. Besides that an implementation of the algorithm is given in the subsequent work.…

We devise a polynomial-time approximation scheme for the classical geometric problem of finding an approximate short path amid weighted regions. In this problem, a triangulated region P comprising of n vertices, a positive weight associated…

Let $P$ be a polygon with $r>0$ reflex vertices and possibly with holes and islands. A subsuming polygon of $P$ is a polygon $P'$ such that $P \subseteq P'$, each connected component $R$ of $P$ is a subset of a distinct connected component…

We give a polynomial-time algorithm that, with input a graph $G$ and two vertices $u,v$ of $G$, decides whether there is an induced $uv$-path that is longer than the shortest $uv$-path.

Many robotics applications benefit from being able to compute multiple locally optimal paths in a given configuration space. Examples include path planning for of tethered robots with cable-length constraints, systems involving cables,…

We perform an experimental evaluation of algorithms for finding geodesic shortest paths between two points inside a simple polygon in the constant-workspace model. In this model, the input resides in a read-only array that can be accessed…

We provide a solution method for the polyhedral convex set optimization problem, that is, the problem to minimize a set-valued mapping with polyhedral convex graph with respect to a set ordering relation which is generated by a polyhedral…

We present algorithms for multi-modal route planning in road and public transit networks, as well as in combined networks. Therefore, we explore the nearest neighbor and shortest path problem and propose solutions based on Cover-Trees, ALT…

Autonomous agents face the challenge of coordinating multiple tasks (perception, motion planning, controller) which are computationally expensive on a single onboard computer. To utilize the onboard processing capacity optimally, it is…

Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…

We address the point-to-face approximate shortest path problem in R: Given a set of polyhedral obstacles with a total of n vertices, a source point s, an obstacle face f, and a real positive parameter epsilon, compute a path from s to f…

The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…

Contour polygonal approximation is a simplified representation of a contour by line segments, so that the main characteristics of the contour remain in a small number of line segments. This paper presents a novel method for polygonal…

In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and…

Cutting-planes are one of the most important building blocks for solving large-scale integer programming (IP) problems to (near) optimality. The majority of cutting plane approaches rely on explicit rules to derive valid inequalities that…

A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…

A new algorithm of the canonical polyadic decomposition (CPD) presented here. It features lower computational complexity and memory usage than the available state of the art implementations. We begin with some examples of CPD applications…