Related papers: Improved Shortest Path Maps with GPU Shaders
Computing shortest path distances between nodes lies at the heart of many graph algorithms and applications. Traditional exact methods such as breadth-first-search (BFS) do not scale up to contemporary, rapidly evolving today's massive…
Very recently a new algorithm to the nonnegative single-source shortest path problem on road networks has been discovered. It is very cache-efficient, but only on static road networks. We show how to augment it to the time-dependent…
Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case.…
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…
For the task of moving a group of indistinguishable agents on a connected graph with unit edge lengths into an arbitrary goal formation, it was previously shown that distance optimal paths can be scheduled to complete with a tight…
Shortest path algorithms have played a key role in the past century, paving the way for modern day GPS systems to find optimal routes along static systems in fractions of a second. One application of these algorithms includes optimizing the…
Querying the shortest path between two vertexes is a fundamental operation in a variety of applications, which has been extensively studied over static road networks. However, in reality, the travel costs of road segments evolve over time,…
This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max_cut problem and the…
We advertise the use of tetrahedral grids constructed via the longest edge bisection algorithm for rendering volumetric data with path tracing. The key benefits of such grids is two-fold. First, they provide a highly adaptive…
Computing shortest paths is a fundamental operation in processing graph data. In many real-world applications, discovering shortest paths between two vertices empowers us to make full use of the underlying structure to understand how…
We present a method for path optimization for ground vehicles in off-road environments at high speeds. This path optimization considers the kinematic constraints of the vehicle. By thinking in the actuator space we can represent these…
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to…
We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One…
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…
The bi-objective shortest-path (BOSP) problem seeks to find paths between start and target vertices of a graph while optimizing two conflicting objective functions. We consider the BOSP problem in the presence of correlated objectives. Such…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely:…
In this paper we consider discrete robot path planning problems on metric graphs. We propose a clustering method, Gamma-Clustering for the planning graph that significantly reduces the number of feasible solutions, yet retains a solution…
Consider a general path planning problem of a robot on a graph with edge costs, and where each node has a Boolean value of success or failure (with respect to some task) with a given probability. The objective is to plan a path for the…
We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path…