Finding minimum area simple pentagons

Given a set P of n points in the plane, we want to find a simple, not necessarily convex, pentagon Q with vertices in P of minimum area. We present an algorithm for solving this problem in time O( nT( n)) and space O( n), where T( n) is the number of empty triangles in the set.

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Bibliographic Details
Published inOperations research letters Vol. 21; no. 5; pp. 229 - 233
Main Authors Hêche, Jean-François, Liebling, Thomas M.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 1997
Elsevier
Subjects
Applied sciences
Exact sciences and technology
Minimum area
Operational research and scientific management
Operational research. Management science
Optimization. Search problems
Pentagons
Polynomial algorithms
Polynomial algorithms
Minimum area
Pentagons
Algorithms
Pentagonal shape
Optimization
Polynomial time
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Summary:Given a set P of n points in the plane, we want to find a simple, not necessarily convex, pentagon Q with vertices in P of minimum area. We present an algorithm for solving this problem in time O( nT( n)) and space O( n), where T( n) is the number of empty triangles in the set.
ISSN:0167-6377
1872-7468
DOI:10.1016/S0167-6377(97)00051-5