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

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FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2245))

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 logH) 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 · (logH + log log n)) time deterministic algorithm for the problem, that achieves O(n logH) work bound for H = Ω(log n). We present a fast randomized algorithm that runs in expected time O(logH · log n) with high probability and does O(n logH) 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 hold with high probability.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Hansraj College, Delhi University, 110007, New Delhi, India

    Neelima Gupta

  2. Department of Computer Science, Hansraj College, Delhi University, 110007, New Delhi, India

    Sumit Chopra

  3. Department of Computer Science and Engineering, IIT Delhi, 110016, New Delhi, India

    Sandeep Sen

Authors
  1. Neelima Gupta
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  2. Sumit Chopra
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  3. Sandeep Sen
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Automation, Indian Institute of Science, 560012, Bangalore, India

    Ramesh Hariharan  & V. Vinay  & 

  2. Chennai Mathematical Institute, 92 G.N. Chetty Road, 600 017, Chennai, India

    Madhavan Mukund

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© 2001 Springer-Verlag Berlin Heidelberg

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Gupta, N., Chopra, S., Sen, S. (2001). Optimal, Output-Sensitive Algorithms for Constructing Upper Envelope of Line Segments in Parallel. In: Hariharan, R., Vinay, V., Mukund, M. (eds) FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2001. Lecture Notes in Computer Science, vol 2245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45294-X_16

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  • DOI: https://doi.org/10.1007/3-540-45294-X_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43002-5

  • Online ISBN: 978-3-540-45294-2

  • eBook Packages: Springer Book Archive

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