Optimal, Output-Sensitive Algorithms for Constructing Upper Envelope of Line Segments in Parallel

Authors:
Neelima Gupta;Sumit Chopra;Sandeep Sen
Affiliations:
-;-;-
Venue:
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
Year:
2001

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Abstract

In this paper we focus on the problem of designing very fast parallel algorithms for constructing the upper envelope of straight-line segments that achieve the O(n log H) work-bound for input size n and output size H. Our algorithms are designed for the arbitrary CRCW PRAM model. We first describe an O(log n ċ (log H + log log n)) time deterministic algorithm for the problem, that achieves O(n log H) work boundfor H = Ω(log n). We present a fast randomized algorithm that runs in expectedtime O(log H ċ log log n) with high probability and does O(n log H) work. For log H = Ω(log log n), we can achieve the running time of O(log H) while simultaneously keeping the work optimal. We also present a fast randomized algorithm that runs in Õ(log n/ log k) time with nk processors, k logΩ(1) n. The algorithms do not assume any input distribution and the running times holdwith high probability.