Sampling-based bottleneck pathfinding with applications to Frechet matching

TL;DR

This paper introduces a probabilistic sampling-based framework for finding minimal bottleneck paths in high-dimensional spaces, applicable to Frechet distance problems and monotone path constraints, inspired by robot motion planning techniques.

Contribution

It presents a novel, simple, and efficient sampling-based method for bottleneck pathfinding that handles monotonicity constraints, extending existing approaches to more complex problems.

Findings

Framework effectively finds minimal bottleneck paths in various scenarios.

Handles monotone path constraints in high-dimensional spaces.

Experimental results demonstrate practical applicability and efficiency.

Abstract

We describe a general probabilistic framework to address a variety of Frechet-distance optimization problems. Specifically, we are interested in finding minimal bottleneck-paths in $d$-dimensional Euclidean space between given start and goal points, namely paths that minimize the maximal value over a continuous cost map. We present an efficient and simple sampling-based framework for this problem, which is inspired by, and draws ideas from, techniques for robot motion planning. We extend the framework to handle not only standard bottleneck pathfinding, but also the more demanding case, where the path needs to be monotone in all dimensions. Finally, we provide experimental results of the framework on several types of problems.