Algorithms for the Frame of a Finitely Generated Unbounded Polyhedron

Authors:
Jos H. Dul;Francisco J. Lpez
Affiliations:
School of Business, Virginia Commonwealth University, Richmond, Virginia 23284, USA;Department of Information and Decision Sciences, College of Business Administration, University of Texas at El Paso, El Paso, Texas 79968-0544, USA
Venue:
INFORMS Journal on Computing
Year:
2006

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Abstract

Consider two finite sets Ascript and Vscript of points in m-dimensional space. The convex hull of Ascript and the conical hull of Vscript can be combined to create a finitely generated unbounded polyhedron. We explore the geometry of these polyhedral sets to design, implement, test, and compare two different algorithms for finding the frame, a minimal-cardinality subset of Ascript and Vscript, that generates the same polyhedron. One algorithm is a naive approach based on the direct application of the definition of these sets. The second algorithm is based on different principles erecting the frame geometrically one element at a time. Testing indicates that the second algorithm is faster with the difference becoming increasingly dramatic as the cardinality of the sets Ascript and Vscript increases and frame density decreases.