On strongly polynomial variants of the network simplex algorithm for the maximum flow problem

1991 ◽  
Vol 10 (7) ◽  
pp. 383-387 ◽  
Author(s):  
Donald Goldfarb ◽  
Jianxiu Hao
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Simplex Algorithm ◽  
Maximum Flow Problem ◽  
Network Simplex Algorithm ◽  
Network Simplex ◽  
Strongly Polynomial

Use of dynamic trees in a network simplex algorithm for the maximum flow problem

1991 ◽  
Vol 50 (1-3) ◽  
pp. 277-290 ◽  
Author(s):  
Andrew V. Goldberg ◽  
Michael D. Grigoriadis ◽  
Robert E. Tarjan
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Simplex Algorithm ◽  
Maximum Flow Problem ◽  
Network Simplex Algorithm ◽  
Dynamic Trees ◽  
Network Simplex

Strongly polynomial dual simplex methods for the maximum flow problem

1998 ◽  
Vol 80 (1) ◽  
pp. 17-33 ◽  
Author(s):  
Ronald D. Armstrong ◽  
Wei Chen ◽  
Donald Goldfarb ◽  
Zhiying Jin
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Maximum Flow Problem ◽  
Dual Simplex ◽  
Simplex Methods ◽  
Strongly Polynomial

A new strongly polynomial dual network simplex algorithm

1997 ◽  
Vol 78 (2) ◽  
pp. 131-148 ◽  
Author(s):  
Ronald D. Armstrong ◽  
Zhiying Jin
Keyword(s):  
Simplex Algorithm ◽  
Network Simplex Algorithm ◽  
Network Simplex ◽  
Strongly Polynomial

A Combinatorial Algorithm for Generalized Maximum Flow Problem in Lossy Network

2012 ◽  
Vol 263-266 ◽  
pp. 2295-2300
Author(s):  
Li Wei Dong ◽  
Xiaofen Zhang ◽  
Hong Wang
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Dijkstra’S Algorithm ◽  
Combinatorial Algorithm ◽  
Residual Network ◽  
Maximum Flow Problem ◽  
Dijkstra's Algorithm ◽  
Augmenting Path ◽  
Strongly Polynomial

This paper first presents the method for finding a generalized augmenting path according to the idea of Dijkstra's algorithm. Then the combinatorial algorithm for solving the generalized maximum flow is given in lossy network. The algorithm runs in strongly polynomial times by finding the generalized f-augmenting path in a generalized residual network.

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