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On Combinatorial Properties of Linear Program Digraphs David Avis

Summary: On Combinatorial Properties of Linear Program Digraphs
David Avis
Computer Science and GERAD
McGill University
Montreal, Quebec, Canada
Sonoko Moriyama
Institute for Nano Quantum
Information Electronics,
University of Tokyo, Japan
September 13, 2008
The possible pivot operations of the simplex method to solve a linear program can
be represented as a directed graph defined on the skeleton of the feasible region P. We
consider the case that P is bounded, i.e., a convex polytope. The directed graph is called
an LP digraph. LP digraphs are known to satisfy the following three properties: acyclicity,
unique sink orientation(USO), and the Holt-Klee property. The three properties are not
generally sufficient for a directed graph on the skeleton of P to be an LP digraph. In
this paper, we first survey some previous results on LP digraphs, showing relationships


Source: Avis, David - School of Computer Science, McGill University


Collections: Computer Technologies and Information Sciences