# A Counterexample to a Diameter Algorithm for Convex Polygons

Binay K. Bhattacharya, Godfried Toussaint

Research output: Contribution to journalArticle

### Abstract

Recently, Snyder and Tang [1] proposed an algorithm for finding the diameter of a convex polygon. In this note a family of convex polygons is described for which their algorithm fails. It is also pointed out that the diameter of an arbitrary simple n-vertex polygon can be computed in 0(n) time.

Original language English (US) 306-309 4 IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-4 3 https://doi.org/10.1109/TPAMI.1982.4767248 Published - Jan 1 1982

### Fingerprint

Convex polygon
Counterexample
Polygon
Arbitrary
Vertex of a graph
Family

### Keywords

• Algorithm
• artificial intelligence
• computational complexity
• computational geometry
• convex hull
• convex polygon
• image processing
• pattern recognition
• region growing
• scene analysis
• simple polygon

### ASJC Scopus subject areas

• Artificial Intelligence
• Computational Theory and Mathematics
• Computer Vision and Pattern Recognition
• Software
• Applied Mathematics
• Control and Systems Engineering
• Electrical and Electronic Engineering

### Cite this

A Counterexample to a Diameter Algorithm for Convex Polygons. / Bhattacharya, Binay K.; Toussaint, Godfried.

In: IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-4, No. 3, 01.01.1982, p. 306-309.

Research output: Contribution to journalArticle

title = "A Counterexample to a Diameter Algorithm for Convex Polygons",
abstract = "Recently, Snyder and Tang [1] proposed an algorithm for finding the diameter of a convex polygon. In this note a family of convex polygons is described for which their algorithm fails. It is also pointed out that the diameter of an arbitrary simple n-vertex polygon can be computed in 0(n) time.",
keywords = "Algorithm, artificial intelligence, computational complexity, computational geometry, convex hull, convex polygon, image processing, pattern recognition, region growing, scene analysis, simple polygon",
author = "Bhattacharya, {Binay K.} and Godfried Toussaint",
year = "1982",
month = "1",
day = "1",
doi = "10.1109/TPAMI.1982.4767248",
language = "English (US)",
volume = "PAMI-4",
pages = "306--309",
journal = "IEEE Transactions on Pattern Analysis and Machine Intelligence",
issn = "0162-8828",
publisher = "IEEE Computer Society",
number = "3",

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T1 - A Counterexample to a Diameter Algorithm for Convex Polygons

AU - Bhattacharya, Binay K.

AU - Toussaint, Godfried

PY - 1982/1/1

Y1 - 1982/1/1

N2 - Recently, Snyder and Tang [1] proposed an algorithm for finding the diameter of a convex polygon. In this note a family of convex polygons is described for which their algorithm fails. It is also pointed out that the diameter of an arbitrary simple n-vertex polygon can be computed in 0(n) time.

AB - Recently, Snyder and Tang [1] proposed an algorithm for finding the diameter of a convex polygon. In this note a family of convex polygons is described for which their algorithm fails. It is also pointed out that the diameter of an arbitrary simple n-vertex polygon can be computed in 0(n) time.

KW - Algorithm

KW - artificial intelligence

KW - computational complexity

KW - computational geometry

KW - convex hull

KW - convex polygon

KW - image processing

KW - pattern recognition

KW - region growing

KW - scene analysis

KW - simple polygon

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M3 - Article

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VL - PAMI-4

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EP - 309

JO - IEEE Transactions on Pattern Analysis and Machine Intelligence

JF - IEEE Transactions on Pattern Analysis and Machine Intelligence

SN - 0162-8828

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