Abstract. The authors present an O(inn log m) algorithm for solving feasibility in linear programs with up to two variables per inequality which is derived directly from the Fourier-Motzkin elimination method. (The number of variables and inequalities are denoted by n and m, respectively.) The running time of the algorithm dominates that of the best known algorithm for the problem, and is far simpler. Integer programming on monotone inequalities, i.e., inequalities where the coefficients are of opposite sign, is then considered. This problem includes as a special case the simultaneous approximation of a rational vector with specified accuracy, which is known to be NP-complete. However, it is shown that both a feasible solution and an optimal solution with respect to an arbitrary objective function can be computed in pseudo-polynomial time.
In REF , the Fourier-Motzkin elimination procedure was used to provide a strongly polynomial algorithm, which to date is the fastest known algorithm for this problem.
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
SIAM J. Comput.
SIAM J. Comput.
Mathematics Computer Science