I/O-efficient triangular range search and its application

In this paper, we consider a special type of triangular range search for a planar point set S in the I/O-model. Here, two sides of the query triangle are parallel to the coordinate axes (x- and y-axis). We call such a triangle an axis parallel triangle. For the axis parallel triangular range search problem, we propose a data structure of size O(N B ( log1+ B N logB logB N )2 ) disk blocks and a query algorithm of complexity O(logB N( logB N logB logB N )2 + K/B) I/Os, where 0 < < 1, N is the number of points in S, B is the number of points transferred in one I/O, and K is the number of points in the answer to the query. We also consider the application of this data structure and query algorithm to oriented rectangular range search.

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Gautam K. Das, Bradford G. Nickerson
• Keywords: Axis Parallel, CCCG 2010, Computational Geometry, Query Algorithm, Triangular Range Search