Polynomial Algorithms for Totally Dual Integral Systems and Extensions

Publisher Summary This chapter discusses integer (linear) programs that have the property that for every integral right-hand side vector for which the linear program (obtained by dropping the integrality requirement) has an optimal value for the objective function, the optimal value of the integer program differs from that for the linear program by at most a fraction. This class properly includes totally dual integral (TDI) systems, along with many other cases. In addition, the chapter provides a unified basis for algorithms that involve the solving of one linear program for TDI systems. Set packing problems are also reviewed in the chapter.