This paper shows that the minimum ratio cancelingalgorithm of Wallacher (Unpublished manuscript, Institut fur Ange-wandte Mathematik, Technische Universitat, Braunschweig (1989)) (and a faster relaxed version) can be...
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This paper shows that the minimum ratio cancelingalgorithm of Wallacher (Unpublished manuscript, Institut fur Ange-wandte Mathematik, Technische Universitat, Braunschweig (1989)) (and a faster relaxed version) can be generalized to an algorithm for general linear programs with geometric convergence. This implies that when we have a negativecycle oracle, this algorithm will compute an optimal solution in (weakly) polynomial time. We then specialize the algorithm to linear programming on unimodular linear spaces, and to the minimum cost flow and (dual) tension problems. We construct instances proving that even in the network special cases the algorithm is not strongly polynomial. (C) 2000 Elsevier Science B.V. All rights reserved.
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