Chromatic distribution of k-nearest neighbors of a line segment in a planar colored point set

Authors:
Partha P. Goswami;Sandip Das;Subhas C. Nandy
Affiliations:
Calcutta University, Calcutta 700 0073, India;Indian Statistical Institute, Calcutta 700 108, India;Indian Statistical Institute, Calcutta 700 108, India
Venue:
Information Processing Letters
Year:
2007

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Abstract

Let P be a set of n colored points distributed arbitrarily in R^2. The chromatic distribution of the k-nearest neighbors of a query line segment @? is to report the number of points of each color among the k-nearest points of the query line segment. While solving this problem, we have encountered another interesting problem, namely the semicircular range counting query. Here a set of n points is given. The objective is to report the number of points inside a given semicircular range. We propose a simple algorithm for this problem with preprocessing time and space complexity O(n^3), and the query time complexity O(logn). Finally, we propose the algorithm for reporting the chromatic distribution of k nearest neighbors of a query line segment. Using our proposed technique for semicircular range counting query, it runs in O(log^2n) time.