On the multimodality of distances in convex polygons

David Avis, Godfried Toussaint, Binay K. Bhattacharya

Research output: Contribution to journalArticle

Abstract

Examples are given of n vertex convex polygons for which the distances between a fixed vertex and the remaining vertices, visited in order, form a multi-modal function. We show that this function may have as many as n/2 modes, or local maxima. Further examples are given of n vertex convex polygons in which n2/8 pairs of vertices are local maxima of their corresponding distance functions. These results are used to construct an example that shows that a general algorithm of Dobkin and Snyder may not, in fact, be used to find the diameter of a convex polygon.

Original languageEnglish (US)
Pages (from-to)153-156
Number of pages4
JournalComputers and Mathematics with Applications
Volume8
Issue number2
DOIs
StatePublished - Jan 1 1982

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Multimodality
Convex polygon
Vertex of a graph
Multimodal Function
Distance Function

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modeling and Simulation

Cite this

On the multimodality of distances in convex polygons. / Avis, David; Toussaint, Godfried; Bhattacharya, Binay K.

In: Computers and Mathematics with Applications, Vol. 8, No. 2, 01.01.1982, p. 153-156.

Research output: Contribution to journalArticle

Avis, David ; Toussaint, Godfried ; Bhattacharya, Binay K. / On the multimodality of distances in convex polygons. In: Computers and Mathematics with Applications. 1982 ; Vol. 8, No. 2. pp. 153-156.
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