Introduction and preliminaries; Problems, algorithms, and complexity. Linear algebra; Linear algebra and complexity; Notes on linear algebra; Lattices and linear diophantine equations; Theory of lattices and linear diophantine equations; Algorithms for linear diophantine equations; Diophantine approximations and basis reduction; Notes on lattices and linear diophantine equations; Polyhedra, linear inequalities, and linear programming; Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; The structure of polyhedra; Polarity, and blocking and anti-blocking polyhedra; Sizes and the theoretical complexity of linear inequalities and linear programming; The simplex method; Primal-dual, elimination, and relaxation methods; Khachiyan's method for linear programming; The ellipsoid method for polyhedra more generally; Further polynomiality results in linear programming; Notes on polyhedra, linear inequalities, and linear programming; Integer linear programming; Introduction to integer linear programming; Estimates in integer linear programming; The complexity of integer linear programming; Totally unimodular matrices: fundamental properties and examples; Recognizing total unimodularity; Further theory related to total unimodularity; Integral polyhedra and total dual integrality; Cutting planes; Further methods in integer linear programming; Historical and further notes on integer linear programming; References.II, Canadian Journal of Mathematics 13 (1961) 346-352 [reprinted in: Paul Erdos. The Art of ...  Eves, H. (1966), Elementary Matrix Theory, Allyn and Bacon, Boston, Mass., 1966.  Faaland, B. (1972), On the number of solutions to a diophantine equation, Journal of Combinatorial Theory (A) 13 (1972) 170-175.
|Title||:||Theory of linear and integer programming|
|Publisher||:||John Wiley & Sons Inc - 1986-12-29|