Related papers: Exact Wavefront Propagation for Globally Optimal O…
This paper introduces a novel, lightweight method to solve the visibility problem for 2D grids. The proposed method evaluates the existence of lines-of-sight from a source point to all other grid cells in a single pass with no preprocessing…
Path planning and obstacle avoidance are the two major issues in any navigation system. Wavefront propagation algorithm, as a good path planner, can be used to determine an optimal path. Obstacle avoidance can be achieved using possibility…
We propose a path-guiding algorithm to be incorporated into the wavefront style of path tracers (WFPTs). As WFPTs are primarily implemented on graphics processing units (GPUs), the proposed method aims to leverage the capabilities of the…
We present a novel algorithm for dynamic routing with dedicated path protection which, as the presented simulation results suggest, can be efficient and exact. We present the algorithm in the setting of optical networks, but it should be…
This paper presents a novel method for accelerating path-planning tasks in unknown scenes with obstacles by utilizing Wasserstein Generative Adversarial Networks (WGANs) with Gradient Penalty (GP) to approximate the distribution of…
Hierarchical, multi-resolution volumetric mapping approaches are widely used to represent large and complex environments as they can efficiently capture their occupancy and connectivity information. Yet widely used path planning methods…
The Dijkstra algorithm is a classic path planning method, which in a discrete graph space, can start from a specified source node and find the shortest path between the source node and all other nodes in the graph. However, to the best of…
Learning for robot navigation presents a critical and challenging task. The scarcity and costliness of real-world datasets necessitate efficient learning approaches. In this letter, we exploit Euclidean symmetry in planning for 2D…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
We analyze two algorithms for approximating the general optimal transport (OT) distance between two discrete distributions of size $n$, up to accuracy $\varepsilon$. For the first algorithm, which is based on the celebrated Sinkhorn's…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
We present a global optimization approach to optical flow estimation. The approach optimizes a classical optical flow objective over the full space of mappings between discrete grids. No descriptor matching is used. The highly regular…
In this paper, we address the problem of efficient execution of a computation pattern, referred to here as the irregular wavefront propagation pattern (IWPP), on hybrid systems with multiple CPUs and GPUs. The IWPP is common in several…
We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n…
This paper proposes a solution to the problem of smooth path planning for mobile robots in dynamic and unknown environments. A novel concept of Time-Warped Grid is introduced to predict the pose of obstacles in the environment and avoid…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
Dispersion of mobile robots over the nodes of an anonymous graph is an important problem and turns out to be a crucial subroutine for designing efficient algorithms for many fundamental graph problems via mobile robots. In this problem,…
We present algorithms for solving high-frequency acoustic scattering problems in complex domains. The eikonal and transport partial differential equations from the WKB/geometric optic approximation of the Helmholtz equation are solved…
We present a new $4$-approximation algorithm for the Combinatorial Motion Planning problem which runs in $\mathcal{O}(n^2\alpha(n^2,n))$ time, where $\alpha$ is the functional inverse of the Ackermann function, and a fully distributed…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…