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.

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

scholarly journals A Parametric Network Approach for Concepts Hierarchy Generation in Text Corpus

2016 ◽  
Vol 24 (1) ◽  
pp. 371-381
Author(s):  
L. S. Sângeorzan ◽  
M. M. Parpalea ◽  
M. Parpalea
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Network Approach ◽  
Residual Network ◽  
Text Corpus ◽  
Maximum Flow Problem ◽  
Directed Paths ◽  
Parametric Network ◽  
Parameter Values ◽  
Hierarchy Generation

Abstract The article presents a preflow approach for the parametric maximum flow problem, derived from the rules of constructing concepts hierarchy in text corpus. Just as generating a taxonomy can be equivalently reduced to ranking concepts within a text corpus according to a defined criterion, the proposed preflow bipush-relabel algorithm computes the maximum flow - the optimum ow that respects certain ranking constraints. The parametric preflow algorithm for generating two level concepts hierarchy in text corpus works in a parametric bipartite association network and, on each step, the maximum possible amount of ow is pushed along conditional augmenting two-arcs directed paths in the parametric residual network, for the maximum interval of the parameter values. The obtained parametric maximum ow generates concepts hierarchies (taxonomies) in text corpus for different degrees of association values described by the parameter values.

scholarly journals Maximum Network Flow Algorithms

2021 ◽  
Vol 6 ◽  
pp. 75-81
Author(s):  
Mohan Chandra Adhikari ◽  
Umila Pyakurel
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Dynamic Networks ◽  
Maximum Flow ◽  
Incoming Flow ◽  
Network Flow Problem ◽  
Maximum Flow Problem ◽  
Augmenting Path ◽  
Families First ◽  
Maximum Network Flow

The aim of the maximum network flow problem is to push as much flow as possible between two special vertices, the source and the sink satisfying the capacity constraints. For the solution of the maximum flow problem, there exists a number of algorithms. The existing algorithms can be divided into two families. First, augmenting path algorithms that satisfy the conservation constraints at intermediate vertices and the second preflow push relabel algorithms that violates the conservation constraints at the intermediate vertices resulting incoming flow more than outgoing flow.In this paper, we study different algorithms that determine the maximum flow in the static and dynamic networks.

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.

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