On-line and off-line vertex enumeration by adjacency lists

Authors:
Pey-Chun Chen;Pierre Hansen;Brigitte Jaumard
Affiliations:
RUTCOR - Rutgers Center for Operations Research, Rutgers, the State University of New Jersey, New Brunswick, NJ 08903, USA;RUTCOR - Rutgers Center for Operations Research, Rutgers, the State University of New Jersey, New Brunswick, NJ 08903, USA;GERAD and École Polytechnique de Montréal, Case Postale 6079, Succursale A, Montréal, Canada H3C 3A7
Venue:
Operations Research Letters
Year:
1991

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Abstract

We propose a new algorithm to solve the on-line vertex enumeration problem for polytopes, doing all computations in n-space, where n is the dimension of the polytope. This algorithm exploits adjacency lists between vertices and uses no simplex tableaux. It can handle the cases of empty or degenerate polyhedra. A theoretical and numerical comparison with existing approaches for off-line vertex enumeration is presented.