Triangular range counting query in 2D and its application in finding k nearest neighbors of a line segment

Authors:
Partha P. Goswami;Sandip Das;Subhas C. Nandy
Affiliations:
Computer Center, Calcutta University, Kolkata, 700 029, India;ACM Unit, Indian Statistical Institute, Kolkata, 700 108, India;ACM Unit, Indian Statistical Institute, Kolkata, 700 108, India
Venue:
Computational Geometry: Theory and Applications
Year:
2004

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Abstract

We present an efficient algorithm for finding k nearest neighbors of a query line segment among a set of points distributed arbitrarily on a two dimensional plane. Along the way to finding this algorithm, we have obtained an improved triangular 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, such that given a triangular query region Δ, the number of points inside Δ can be reported in O(logn) time. Finally, this triangular range counting technique is used for finding k nearest neighbors of a query straight line segment in O(log2 n + k) time.