Abstract
We present an efficient algorithm for finding k nearest neighbours of a query line segment among a set of points 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(n 2) time and space, which reports the number of points inside a query triangular region Δ in O(logn) time. The members of P inside Δ can be reported in O(log2 n + κ) time, where κ is the size of the output. Finally, this technique is used to find k nearest neighbors of a query straight line segment in O(log2 n + k) time.
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© 2002 Springer-Verlag Berlin Heidelberg
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Goswami, P.P., Das, S., Nandy, S.C. (2002). Simplex Range Searching and k Nearest Neighbors of a Line Segment in 2D. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_8
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DOI: https://doi.org/10.1007/3-540-45471-3_8
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