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In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…

In this work we consider algorithms for reconstructing time-varying data into a finite sum of discrete trajectories, alternatively, an off-the-grid sparse-spikes decomposition which is continuous in time. Recent work showed that this…

Factor graph optimization serves as a fundamental framework for robotic perception, enabling applications such as pose estimation, simultaneous localization and mapping (SLAM), structure-from-motion (SfM), and situational awareness.…

We consider an optimal flow distribution problem in which the goal is to find a radial configuration that minimizes resistance-induced quadratic distribution costs while ensuring delivery of inputs from multiple sources to all sinks to meet…

Problem of finding 2D paths of special shape, e.g. paths comprised of line segments having the property that the angle between any two consecutive segments does not exceed the predefined threshold, is considered in the paper. This problem…

We consider the problem of computing shortest paths in a dense motion-planning roadmap $\mathcal{G}$. We assume that~$n$, the number of vertices of $\mathcal{G}$, is very large. Thus, using any path-planning algorithm that directly searches…

Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…

We present the generic Dijkstra shortest path algorithm: an efficient algorithm for finding a shortest path in an optical network, both in a wavelength-division multiplexed network, and an elastic optical network (EON). The proposed…

Many disciplines of science and engineering deal with problems related to compositions, ranging from chemical compositions in materials science to portfolio compositions in economics. They exist in non-Euclidean simplex spaces, causing many…

Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…

This paper explores a rapid, optimal smooth path-planning algorithm for robots (e.g., autonomous vehicles) in point cloud environments. Derivative maps such as dense point clouds, mesh maps, Octomaps, etc. are frequently used for path…

In this paper, we present exact exponential algorithms for computing branchwidth that are fast both in theory and in practice. The running times of these algorithms are single-exponential in the number of vertices. Our basic algorithm is…

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…

The 1-median problem (1MP) on undirected weighted graphs seeks to find a facility location minimizing the total weighted distance to all customer nodes. Although the 1MP can be solved exactly by computing the single-source shortest paths…

This paper presents a novel method for real-time 3D navigation in large-scale, complex environments using a hierarchical 3D visibility graph (V-graph). The proposed algorithm addresses the computational challenges of V-graph construction…

We present highly efficient algorithms for performing forward and backward propagation of Convolutional Neural Network (CNN) for pixelwise classification on images. For pixelwise classification tasks, such as image segmentation and object…

The dual of a planar graph $G$ is a planar graph $G^*$ that has a vertex for each face of $G$ and an edge for each pair of adjacent faces of $G$. The profound relationship between a planar graph and its dual has been the algorithmic basis…

This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…

This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…

We present a centralized algorithmic framework for solving multi-robot path planning problems in general, two-dimensional, continuous environments while minimizing globally the task completion time. The framework obtains high levels of…