an:04018765
Zbl 0626.90053
Tardos, ??va
A strongly polynomial algorithm to solve combinatorial linear programs
EN
Oper. Res. 34, 250-256 (1986).
00151822
1986
j
90C05 68Q25 90C27 90C06 65K05
polynomial linear programming algorithm; minimum cost flow; multicommodity flow problems
A polynomial linear programming algorithm that solves max(cx: \(x\geq 0\), \(Ax=b)\) is proposed. The algorithm consists of the elementary arithmetic operations only, and the number of those operations depends only on the size of the entries (being, in fact, rational numbers) in the constraint matrix A. On the other hand the complexity of the algorithm is independent of the size of the entries in c and of those in b. The algorithm can be applied to solve the minimum cost flow and the multicommodity flow problems.
W.Stanczak