Related papers: Off-lattice and parallel implementations of the pi…
Realistic path planning applications often require optimizing with respect to several criteria simultaneously. Here we introduce an efficient algorithm for bi-criteria path planning on graphs. Our approach is based on augmenting the state…
Downsampling and path planning are essential in robotics and autonomous systems, as they enhance computational efficiency and enable effective navigation in complex environments. However, current downsampling methods often fail to preserve…
We propose a new algorithm for numerical path tracking in polynomial homotopy continuation. The algorithm is `robust' in the sense that it is designed to prevent path jumping and in many cases, it can be used in (only) double precision…
Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting lattice points inside a polytope. However, state-of-the-art algorithms for this problem…
Efficient motion planning algorithms are essential in robotics. Optimizing essential parameters, such as batch size and nearest neighbor selection in sampling-based methods, can enhance performance in the planning process. However, existing…
Flat histogram methods, such as Wang--Landau sampling, provide a means for high-throughput calculation of phase diagrams of atomistic/lattice model systems. Many parallelisation schemes with varying degrees of complexity have been proposed…
Elimination algorithms for bandit identification, which prune the plausible correct answers sequentially until only one remains, are computationally convenient since they reduce the problem size over time. However, existing elimination…
Existing parallel algorithms for wavelet tree construction have a work complexity of $O(n\log\sigma)$. This paper presents parallel algorithms for the problem with improved work complexity. Our first algorithm is based on parallel integer…
We approach the fundamental problem of obstacle avoidance for robotic systems via the lens of online learning. In contrast to prior work that either assumes worst-case realizations of uncertainty in the environment or a stationary…
A new path planning method for Mobile Robots (MR) has been developed and implemented. On the one hand, based on the shortest path from the start point to the goal point, this path planner can choose the best moving directions of the MR,…
Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…
We propose three novel gerrymandering algorithms which incorporate the spatial distribution of voters with the aim of constructing gerrymandered, equal-population, connected districts. Moreover, we develop lattice models of voter…
The credit on {\it reduction theory} goes back to the work of Lagrange, Gauss, Hermite, Korkin, Zolotarev, and Minkowski. Modern reduction theory is voluminous and includes the work of A. Lenstra, H. Lenstra and L. Lovasz who created the…
Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive,…
We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…
Path planners based on basic rapidly-exploring random trees (RRTs) are quick and efficient, and thus favourable for real-time robot path planning, but are almost-surely suboptimal. In contrast, the optimal RRT (RRT*) converges to the…
Random walks are a fundamental primitive used in many machine learning algorithms with several applications in clustering and semi-supervised learning. Despite their relevance, the first efficient parallel algorithm to compute random walks…
In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…
In Reinforcement Learning (RL), enhancing sample efficiency is crucial, particularly in scenarios when data acquisition is costly and risky. In principle, off-policy RL algorithms can improve sample efficiency by allowing multiple updates…
Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations.…