ENUMERATION OF ALL SOLUTIONS OF A COMBINATORIAL LINEAR INEQUALITY SYSTEM ARISING FROM THE POLYHEDRAL HOMOTOPY CONTINUATION METHOD
Akiko Takeda, Masakazu Kojima, Katsuki Fujisawa · Journal of the Operations Research Society of Japan · 2002
An interesting combinatorial (enumeration) problem arises in the initial phase of the polyhedral homotopy continuation method for computing all solutions of a polynomial equation system in complex variables. It is formulated as a problem of finding all solutions of a specially structured system of linear inequalities with a certain additional combinatorial condition. This paper presents a computational method for the problem fully utilizing the duality theory and the simplex method for linear programs, and report numerical results on a single cpu implementation and a parallel cpu implementation of the method.