an:06093763
Zbl 1268.90029
Chubanov, Sergei
A strongly polynomial algorithm for linear systems having a binary solution
EN
Math. Program. 134, No. 2 (A), 533-570 (2012).
00307257
2012
j
90C05 90C09
linear programming; polynomial algorithm; integer solutions
The paper describes a strongly polynomial algorithm which either finds a solution to a linear system with integer coefficients, or correctly decides that the system does not have 0,1-solutions. The algorithm can be used as a basis for the construction of a polynomial algorithm for linear programming, which differs substantially from the well-known polynomial algorithms. The most important properties on which the method is based are the (Hahn-Banach) separation theorem for disjoint convex sets and the Cauchy-Schwarz inequality.
Maxim Ivanov Todorov (San Andres Cholula)