Related papers: Group Marching Tree: Sampling-Based Approximately …
Path planning in robotics often involves solving continuously valued, high-dimensional problems. Popular informed approaches include graph-based searches, such as A*, and sampling-based methods, such as Informed RRT*, which utilize informed…
We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…
In this paper we study a scheduling problem arising from executing numerical simulations on HPC architectures. With a constant number of parallel machines, the objective is to minimize the makespan under memory constraints for the machines.…
This paper proposes a new optimal control synthesis algorithm for multi-robot systems under global temporal logic tasks. Existing planning approaches under global temporal goals rely on graph search techniques applied to a product automaton…
Sampling-based motion-planning algorithms typically rely on nearest-neighbor (NN) queries when constructing a roadmap. Recent results suggest that in various settings NN queries may be the computational bottleneck of such algorithms.…
Recent progress in randomized motion planners has led to the development of a new class of sampling-based algorithms that provide asymptotic optimality guarantees, notably the RRT* and the PRM* algorithms. Careful analysis reveals that the…
Informed sampling techniques accelerate the convergence of sampling-based motion planners by biasing sampling toward regions of the state space that are most likely to yield better solutions. However, when the current solution path contains…
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…
Optimal path planning involves finding a feasible state sequence between a start and a goal that optimizes an objective. This process relies on heuristic functions to guide the search direction. While a robust function can improve search…
Group-based reinforcement learning algorithms such as Group Reward Policy Optimization (GRPO) have proven effective for fine-tuning large language models (LLMs) with human feedback. However, generating and storing multiple responses per…
Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a…
There is a growing interest in leveraging GPUs for tasks beyond ML, especially in database systems. Despite the existing extensive work on GPU-based database operators, several questions are still open. For instance, the performance of…
Algorithms for dynamically maintaining minimum spanning trees (MSTs) have received much attention in both the parallel and sequential settings. While previous work has given optimal algorithms for dense graphs, all existing parallel…
Optimal path planning aims to determine a sequence of states from a start to a goal while accounting for planning objectives. Popular methods often integrate fixed batch sizes and neglect information on obstacles, which is not…
Path planning in robotics often requires finding high-quality solutions to continuously valued and/or high-dimensional problems. These problems are challenging and most planning algorithms instead solve simplified approximations. Popular…
This paper presents a novel algorithm, called MRRT, which uses multiple rapidly-exploring random trees for fast online replanning of autonomous vehicles in dynamic environments with moving obstacles. The proposed algorithm is built upon the…
In this paper, we present the main features of Dynamic Rapidly-exploring Generalized Bur Tree (DRGBT) algorithm, a sampling-based planner for dynamic environments. We provide a detailed time analysis and appropriate scheduling to facilitate…
Graph Pattern Mining (GPM) is an important, rapidly evolving, and computation demanding area. GPM computation relies on subgraph enumeration, which consists in extracting subgraphs that match a given property from an input graph. Graphics…
This paper proposes a stable sparse rapidly-exploring random trees (SST) algorithm to solve the optimal motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HySST, selects a vertex with the lowest…
We introduce a novel formulation of motion planning, for continuous-time trajectories, as probabilistic inference. We first show how smooth continuous-time trajectories can be represented by a small number of states using sparse Gaussian…