Abstract
Two algorithms to compute the shortest collision-free paths in the Euclidean plane are presented. The ƒ obstacles assumed to be described by disjoint convex polygons having N vertices in total. After preprocessing time O( N+ flog N), a suboptimal shortest path between two arbitrary query points can be found in O( f+ Nlog N) time using Dijkstra's algorithm and in Θ( N) time using the A ∗ algorithm. The space complexity is O( N+ f).
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