Related papers: From Constrained Delaunay Triangulations to Roadma…
This article presents the formal proof of correctness for a plane Delaunay triangulation algorithm. It consists in repeating a sequence of edge flippings from an initial triangulation until the Delaunay property is achieved. To describe…
We present a fast algorithm for the design of smooth paths (or trajectories) that are constrained to lie in a collection of axis-aligned boxes. We consider the case where the number of these safe boxes is large, and basic preprocessing of…
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set $P$ of $n$ points in the plane and a triangulation $G$ that serves as a…
In this paper we study local routing strategies on geometric graphs. Such strategies use geometric properties of the graph like the coordinates of the current and target nodes to route. Specifically, we study routing strategies in the…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
We propose an algorithmic framework for efficient anytime motion planning on large dense geometric roadmaps, in domains where collision checks and therefore edge evaluations are computationally expensive. A large dense roadmap (graph) can…
Finding a shortest path in a graph is one of the most classic problems in algorithmic and graph theory. While we dispose of quite efficient algorithms for this ordinary problem (like the Dijkstra or Bellman-Ford algorithms), some slight…
We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of…
In a rectilinear dual of a planar graph vertices are represented by simple rectilinear polygons and edges are represented by side-contact between the corresponding polygons. A rectilinear dual is called a cartogram if the area of each…
In this paper we address the problem of path planning in an unknown environment with an aerial robot. The main goal is to safely follow the planned trajectory by avoiding obstacles. The proposed approach is suitable for aerial vehicles…
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…
A new interactive approach to navigate on approximations of in general non-convex but connected Pareto fronts is introduced. Given a finite number of precalculated representative Pareto-efficient solutions, an adapted Delaunay triangulation…
Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…
Urban reconstruction from a video captured by a surveying vehicle constitutes a core module of automated mapping. When computational power represents a limited resource and, a detailed map is not the primary goal, the reconstruction can be…
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…
Planar graph navigation is an important problem with significant implications to both point location in geometric data structures and routing in networks. However, whilst a number of algorithms and existence proofs have been proposed, very…
Given a set of basic areas, the territory design problem asks to create a predefined number of territories, each containing at least one basic area, such that an objective function is optimized. Desired properties of territories often…
We present a deterministic local routing algorithm that is guaranteed to find a path between any pair of vertices in a half-$\theta_6$-graph (the half-$\theta_6$-graph is equivalent to the Delaunay triangulation where the empty region is an…
In this paper, we develop a framework for path-planning on abstractions that are not provided to the agent a priori but instead emerge as a function of the available computational resources. We show how a path-planning problem in an…
The problem of constrained coverage path planning involves a robot trying to cover maximum area of an environment under some constraints that appear as obstacles in the map. Out of the several coverage path planning methods, we consider…