论文信息 - A Tight Lower Bound for the Complexity of Path-Planning for a Disc

A Tight Lower Bound for the Complexity of Path-Planning for a Disc

Abstract Given two points in a planar room with polygonal boundary and polygonal obstacles (having a total of n corners), the problem of finding a shortest obstacle-avoiding path between them is known to require Ω(n log n) time. In this article it is shown that the problem of finding any obstacle-avoiding path for a disc in the room, or even deciding whether such a path exists, requires Ω(n log n) time. This bound is met by the published algorithms.

Colm Ó'Dúnlaing

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