Abstract
This note describes some sufficient conditions for the maximum or minimum of a weighted flow (the weights are on paths, and are derived from weights on the edges of the path), of given volume in a series parallel graph to be found by a greedy algorithm.
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Y.P. Aneja, R. Chandrasekaran and K.P.K. Nair, “Classes of linear programs with integral optimal solutions,”Mathematical Programming Study 24 (1985) 225–237.
W.W. Bein, P. Brucker and A. Tamir, “Minimum cost flow algorithms for series-parallel networks,”Discrete Applied Mathematics 10 (1985) 117–124.
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Hoffman, A.J. On greedy algorithms for series parallel graphs. Mathematical Programming 40, 197–204 (1988). https://doi.org/10.1007/BF01580730
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DOI: https://doi.org/10.1007/BF01580730