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Summary: On Combinatorial Properties of Linear Program Digraphs
David Avis
Computer Science and GERAD
McGill University
Montreal, Quebec, Canada
avis@cs.mcgill.ca
Sonoko Moriyama
Institute for Nano Quantum
Information Electronics,
University of Tokyo, Japan
moriso@is.s.u-tokyo.ac.jp
September 13, 2008
Abstract
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
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