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 characterization 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.

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