Listing vertices of simple polyhedra associated with dual LI (2) systems

Authors:
Sammani D. Abdullahi;Martin E. Dyer;Les G. Proll
Affiliations:
School of Computing, University of Leeds, Leeds, UK;School of Computing, University of Leeds, Leeds, UK;School of Computing, University of Leeds, Leeds, UK
Venue:
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Year:
2003

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Abstract

We present an O(nv)Basis Oriented Pivoting (BOP) algorithm for enumerating vertices of simple polyhedra associated with dual LI(2) systems. The algorithm is based on a characterisation of their graphical basis structures, whose set of edges are shown to consist of vertex-disjoint components that are either a tree or a subgraph with only one cycle. The algorithm generates vertices via operations on the basis graph, rather than by simplex transformations.