The MA-ordering max-flow algorithm is not strongly polynomial for directed networks

Authors:
Akiyoshi Shioura
Affiliations:
Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
Venue:
Operations Research Letters
Year:
2004

Citing 3
Cited 0

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Minimum ratio canceling is oracle polynomial for linear programming, but not strongly polynomial, even for networks

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A maximum flow algorithm using MA ordering

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Abstract

Quite recently, Fujishige (Oper. Res. Lett. 31 (2003) 176-178) developed a weakly polynomial-time algorithm for the maximum flow problem by applying the maximum adjacency (MA) ordering technique to directed networks. In this note, we show that the algorithm is not strongly polynomial by giving a real-valued instance for which the algorithm does not terminate.