A primal simplex algorithm that solves the maximum flow problem in at mostnm pivots and O(n 2 m) time

1990 ◽  
Vol 47 (1-3) ◽  
pp. 353-365 ◽  
Author(s):  
Donald Goldfarb ◽  
Jianxiu Hao
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Simplex Algorithm ◽  
Maximum Flow Problem

Efficiency of the Network Simplex Algorithm for the Maximum Flow Problem

1988 ◽  
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 ◽  
Network Simplex

scholarly journals NETWORK SIMPLEX ALGORITHM ASSOCIATED WITH THE MAXIMUM FLOW PROBLEM

2018 ◽  
Vol 104 (1) ◽  
pp. 119-132
Author(s):  
Sennosuke Watanabe ◽  
Hodaka Tanaka ◽  
Yoshihide Watanabe
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Simplex Algorithm ◽  
Maximum Flow Problem ◽  
Network Simplex Algorithm ◽  
Network Simplex

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

Reverse maximum flow problem under the weighted Chebyshev distance

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1107-1121 ◽  
Author(s):  
Javad Tayyebi ◽  
Abumoslem Mohammadi ◽  
Seyyed Mohammad Reza Kazemi
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Binary Search ◽  
Second Phase ◽  
Sink Node ◽  
Search Technique ◽  
Bound Constraints ◽  
Maximum Flow Problem ◽  
Optimal Value ◽  
Two Phases

Given a network G(V, A, u) with two specific nodes, a source node s and a sink node t, the reverse maximum flow problem is to increase the capacity of some arcs (i, j) as little as possible under bound constraints on the modifications so that the maximum flow value from s to t in the modified network is lower bounded by a prescribed value v0. In this paper, we study the reverse maximum flow problem when the capacity modifications are measured by the weighted Chebyshev distance. We present an efficient algorithm to solve the problem in two phases. The first phase applies the binary search technique to find an interval containing the optimal value. The second phase uses the discrete type Newton method to obtain exactly the optimal value. Finally, some computational experiments are conducted to observe the performance of the proposed algorithm.

scholarly journals Engineering Bi-Connected Component Overlay for Maximum-Flow Parallel Acceleration in Large Sparse Graph

2018 ◽  
Vol 36 (5) ◽  
pp. 955-962
Author(s):  
Yang Liu ◽  
Wei Wei ◽  
Heyang Xu
Keyword(s):  
Large Scale ◽  
Flow Problem ◽  
Maximum Flow ◽  
Low Complexity ◽  
Connected Components ◽  
Sparse Graphs ◽  
Fully Integrated ◽  
Flow Acceleration ◽  
Maximum Flow Problem ◽  
Graph Contraction

Network maximum flow problem is important and basic in graph theory, and one of its research directions is maximum-flow acceleration in large-scale graph. Existing acceleration strategy includes graph contraction and parallel computation, where there is still room for improvement:(1) The existing two acceleration strategies are not fully integrated, leading to their limited acceleration effect; (2) There is no sufficient support for computing multiple maximum-flow in one graph, leading to a lot of redundant computation. (3)The existing preprocessing methods need to consider node degrees and capacity constraints, resulting in high computational complexity. To address above problems, we identify the bi-connected components in a given graph and build an overlay, which can help split the maximum-flow problem into several subproblems and then solve them in parallel. The algorithm only uses the connectivity in the graph and has low complexity. The analyses and experiments on benchmark graphs indicate that the method can significantly shorten the calculation time in large sparse graphs.

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