Compact oracles for approximate distances around obstacles in the plane

Authors:
Mikkel Thorup
Affiliations:
AT&T Labs-Research, Shannon Laboratory, Florham Park, NJ
Venue:
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Year:
2007

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Abstract

Consider the Euclidean plane with arbitrary polygonal obstacles with a total of n corners. For arbitrary Ɛ 0, in O(n(log n)3/Ɛ2) time, we construct an O(n(log n)/Ɛ) space oracle that given any two points reports a (1 + Ɛ) approximation of the obstacle avoiding distance in O(1/Ɛ3 + (logn)/(Ɛ log log n)) time. Increasing the oracle space to O(n(log n)2/Ɛ), we can further report a corresponding path in constant time per hop.