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

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. © Springer-Verlag Berlin Heidelberg 2003.