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A fast algorithm for computing sparse visibility graphs

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Abstract

AnO(¦E¦log2 n) algorithm is presented to construct the visibility graph for a collection ofn nonintersecting line segments, where ¦E¦ is the number of edges in the visibility graph. This algorithm is much faster than theO(n 2)-time andO(n 2)-space algorithms by Asanoet al., and by Welzl, on sparse visibility graphs. Thus we partially resolve an open problem raised by Welzl. Further, our algorithm uses onlyO(n) working storage.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Madras, 36, India

    S. Sudarshan & C. Pandu Rangan

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  1. S. Sudarshan
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  2. C. Pandu Rangan
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Communicated by D. T. Lee.

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Sudarshan, S., Pandu Rangan, C. A fast algorithm for computing sparse visibility graphs. Algorithmica 5, 201–214 (1990). https://doi.org/10.1007/BF01840385

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  • DOI: https://doi.org/10.1007/BF01840385

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