Faster output-sensitive parallel algorithms for 3D convex hulls and vector maxima

Authors:
Neelima Gupta;Sandeep Sen
Affiliations:
Department of Computer Science and Engineering, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India;Department of Computer Science and Engineering, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India
Venue:
Journal of Parallel and Distributed Computing
Year:
2003

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Abstract

In this paper we focus on the problem of designing very fast parallel algorithms for the convex hull and the vector maxima problems in three dimensions that are output-size sensitive. Our algorithms achieve O(log log2n log h) parallel time and optimal O(n log h) work with high probability in the CRCW PRAM where n and h are the input and output size, respectively. These bounds are independent of the input distribution and are faster than the previously known algorithms. We also present an optimal speed-up (with respect to the input size only) sublogarithmic time algorithm that uses superlinear number of processors for vector maxima in three dimensions.