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Optimal visibility algorithms for binary images on the hypercube

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Abstract

Consider an×n binary image. Given a directionD, the parallel visibility problem consists of determining for each pixel of the image the portion that is visible (i.e., not obstructed by any other black pixel of the image) in directionD from infinity. A related problem, referred to as point visibility, is to compute for each pixel the portion that is visible from a given pointp. In this paper, we deriveO(logn) time SIMD algorithms for each of these two problems on the hypercube, where one processor is assigned to every pixel of the image. Since the worst case communication distance of two processors in an 2-processor hypercube is 2 logn, it follows that both of the above algorithms are asymptotically optimal.

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Authors and Affiliations

  1. Center for Parallel and Distributed Computing, School of Computer Science, Carleton University, K1S 5B6, Ottawa, Canada

    Frank Dehne

  2. Department 7H65, Bell-Northern Research, P.O. Box 3511, K1Y 4H7, Ottawa, Canada

    Quoc T. Pham

  3. Department of Computer Science, University of Ottawa, K1N 6N5, Ottawa, Canada

    Ivan Stojmenović

Authors
  1. Frank Dehne
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  2. Quoc T. Pham
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  3. Ivan Stojmenović
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Dehne, F., Pham, Q.T. & Stojmenović, I. Optimal visibility algorithms for binary images on the hypercube. Int J Parallel Prog 19, 213–224 (1990). https://doi.org/10.1007/BF01407955

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  • DOI: https://doi.org/10.1007/BF01407955

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