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On the modality of convex polygons

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Under two definitions of random convex polygons, the expected modality of a random convex polygon grows without bound as the number of vertices grows. This refutes a conjecture of Aggarwal and Melville.


  1. 1.

    A. Aggarwal, M. Klawe, S. Moran, D. Shor, and R. Wilber. Geometric applications of a matrix searching algorithm. InProc. 2nd ACM Symposium on Computational Geometry, pp. 285–292, 1986.

  2. 2.

    A. Aggarwal and R. C. Melville. Fast computation of the modality of polygons.J. Algorithms,7:369–381, 1986.

  3. 3.

    D. Avis, G. T. Toussaint, and B. K. Bhattacharya. On the multimodality of distance in convex polygons.Comput. Math. Appl.,8(2):153–156, 1982.

  4. 4.

    D. P. Dobkin and L. Snyder. On a general method for maximizing and minimizing among geometric problems. InProc. 20th Annual Symposium on Foundations of Computer Science, pp. 7–19, 1979.

  5. 5.

    F. P. Preparata and M. I. Shamos.Computational Geometry. Springer-Verlag, New York, 1985.

  6. 6.

    H. Raynaud, Sur l'enveloppe convexe des nuages des points aléatoires dansR n.J. Appl. Probab.,7:35–58, 1970.

  7. 7.

    W. E. Snyder and D. A. Tang. Finding the extrema of a region.IEEE Trans. Pattern Anal. Mach. Intell.,2:266–269, 1980.

  8. 8.

    G. T. Toussaint. Complexity, convexity, and unimodality.Internat. J. Comput. Inform. Sci.,13(3):197–217, 1984.

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Abrahamson, K. On the modality of convex polygons. Discrete Comput Geom 5, 409–419 (1990). https://doi.org/10.1007/BF02187802

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  • Local Maximum
  • Convex Hull
  • Discrete Comput Geom
  • Convex Polygon
  • Blue Region