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18 p, 973.6 KB

A new strongly polynomial dual network simplex algorithm / Armstrong, Ronald D. ; Jin, Zhiying
This paper presents a new dual network simplex algorithm for the minimum cost network flow problem. The algorithm works directly on the original capacitated network and runs in O(mn(m + n log n) log n) time for the network with n nodes and m arcs. [...]
1997
Mathematical Programming, vol. 78 n. 2 (1997) p. 131-148

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21 p, 1.1 MB

A polynomial time primal network simplex algorithm for minimum cost flows / Orlin, James B.
Developing a polynomial time primal network simplex algorithm for the minimum cost flow problem has been a long standing open problem. In this paper, we develop one such algorithm that runs in O(min(n^2m log nC, n^2m^2 log n)) time, where n is the number of nodes in the network, m is the number of arcs, and C denotes the maximum absolute arc costs if arc costs are integer and (infin) otherwise. [...]
1997
Mathematical Programming, vol. 78 n. 2 (1997) p. 109-129

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