Farthest-Point queries with geometric and combinatorial constraints

Authors:
Ovidiu Daescu;Ningfang Mi;Chan-Su Shin;Alexander Wolff
Affiliations:
Department of Computer Science, University of Texas at Dallas, Richardson, TX;Department of Computer Science, College of William and Mary, Williamsburg, VA;School of Electronics and Information Engineering, Hankuk University of Foreign Studies, Korea;Department of Computer Science, Karlsruhe University, Karlsruhe, Germany
Venue:
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Year:
2004

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Abstract

In this paper we discuss farthest-point problems in which a set or sequence S of n points in the plane is given in advance and can be preprocessed to answer various queries efficiently. First, we give a data structure that can be used to compute the point farthest from a query line segment in O(log2n) time. Our data structure needs O(n log n) space and preprocessing time. To the best of our knowledge no solution to this problem has been suggested yet. Second, we show how to use this data structure to obtain an output-sensitive query-based algorithm for polygonal path simplification. Both results are based on a series of data structures for fundamental farthest-point queries that can be reduced to each other.