Simplex Range Searching and k Nearest Neighbors of a Line Segment in 2D

Authors:
Partha P. Goswami;Sandip Das;Subhas C. Nandy
Affiliations:
-;-;-
Venue:
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Year:
2002

Citing 9
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Abstract

We present an efficient algorithm for finding k nearest neighbours ofa query line segment among a set ofp oints distributed arbitrarily on a two dimensional plane. For solving the above, we improved simplex range searching technique in 2D. Given a set of n points, we preprocess them to create a data structure using O(n2) time and space, which reports the number of points inside a query triangular region 驴 in O(logn) time. The members of P inside 驴 can be reported in O(log2n+驴) time, where 驴 is the size ofthe output. Finally, this technique is used to find k nearest neighbors ofa query straight line segment in O(log2n+k) time.