TY - JOUR

T1 - On the multimodality of distances in convex polygons

AU - Avis, David

AU - Toussaint, Godfried T.

AU - Bhattacharya, Binay K.

N1 - Funding Information:
‘iResearch supported by N.S.E.R.C. Grants Nos. A-3013 and A-9293, and F.C.A.C. Grant No. EQ-1678.

PY - 1982

Y1 - 1982

N2 - 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.

AB - 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.

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U2 - 10.1016/0898-1221(82)90054-2

DO - 10.1016/0898-1221(82)90054-2

M3 - Article

AN - SCOPUS:49049144884

VL - 8

SP - 153

EP - 156

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 2

ER -