Query Shortest Paths Amidst Growing Discs
Arash Nouri, Jorg-Rudiger Sack

TL;DR
This paper addresses the problem of finding shortest collision-free paths among growing discs with polynomial growth rates, providing efficient preprocessing and query algorithms for dynamic environments.
Contribution
It introduces a novel approach for shortest path queries amidst polynomially growing discs, extending previous fixed-rate models with efficient preprocessing and query times.
Findings
Preprocessing time is $O(n^2 ext{log} n + k ext{log} k)$.
Query time for shortest path is $O(n^2 ext{log} ( ext{d} n))$.
Number of intersections $k$ is bounded by $O(n^3 ext{d})$.
Abstract
The determination of collision-free shortest paths among growing discs has previously been studied for discs with fixed growing rates. Here, we study a more general case of this problem, where: (1) the speeds at which the discs are growing are polynomial functions of degree , and (2) the source and destination points are given as query points. We show how to preprocess the growing discs so that, for two given query points and , a shortest path from to can be found in time. The preprocessing time of our algorithm is where is the number of intersections between the growing discs and the tangent paths (straight line paths which touch the boundaries of two growing discs). We also prove that .
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Artificial Intelligence in Games · Robotic Path Planning Algorithms
