Shortest path amidst disc obstacles is computable
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
A sweepline algorithm for Euclidean Voronoi diagram of circles
Computer-Aided Design
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We present an algorithm to compute a shortest path for a robot between two points that avoids n discs growing at a common speed in the plane. Our algorithm runs in O(n2 log n) time, thus improving upon the best previous solution by a factor of n. The complexity for the growing disc problem matches the known bound for the more restricted case when the discs are static.