The Maximum Flow and Minimum Cost–Maximum Flow Problems: Computing and Applications

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2020/v7i330185 ◽

2020 ◽

pp. 28-57

Author(s):

W. H. Moolman

Keyword(s):

Network Flow ◽

Transportation Problem ◽

Computer Software ◽

Minimum Cost ◽

Maximum Flow ◽

Flow Diagram ◽

Flow Problems ◽

Real World Problem ◽

Linear Programming Problems ◽

Excel Solver

The maximum flow and minimum cost-maximum flow problems are both concerned with determining flows through a network between a source and a destination. Both these problems can be formulated as linear programming problems. When given information about a network (network flow diagram, capacities, costs), computing enables one to arrive at a solution to the problem. Once the solution becomes available, it has to be applied to a real world problem. The use of the following computer software in solving these problems will be discussed: R (several packages and functions), specially written Pascal programs and Excel SOLVER. The minimum cost-maximum flow solutions to the following problems will also be discussed: maximum flow, minimum cost-maximum flow, transportation problem, assignment problem, shortest path problem, caterer problem.

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Adaptation of Random Binomial Graphs for Testing Network Flow Problems Algorithms

Mathematics ◽

10.3390/math9151716 ◽

2021 ◽

Vol 9 (15) ◽

pp. 1716

Author(s):

Adrian Marius Deaconu ◽

Delia Spridon

Keyword(s):

Network Flow ◽

Large Scale ◽

Random Network ◽

Minimum Cost ◽

Maximum Flow ◽

Network Flow Problems ◽

Commodity Flow ◽

Vast Number ◽

Flow Problems ◽

Execution Speed

Algorithms for network flow problems, such as maximum flow, minimum cost flow, and multi-commodity flow problems, are continuously developed and improved, and so, random network generators become indispensable to simulate the functionality and to test the correctness and the execution speed of these algorithms. For this purpose, in this paper, the well-known Erdős–Rényi model is adapted to generate random flow (transportation) networks. The developed algorithm is fast and based on the natural property of the flow that can be decomposed into directed elementary s-t paths and cycles. So, the proposed algorithm can be used to quickly build a vast number of networks as well as large-scale networks especially designed for s-t flows.

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BINDING ALGORITHM FOR POWER OPTIMIZATION BASED ON NETWORK FLOW METHOD

Journal of Circuits System and Computers ◽

10.1142/s0218126602000422 ◽

2002 ◽

Vol 11 (03) ◽

pp. 259-271 ◽

Cited By ~ 1

Author(s):

YOONSEO CHOI ◽

TAEWHAN KIM

Keyword(s):

Network Flow ◽

Power Optimization ◽

Flow Problem ◽

Minimum Cost ◽

Maximum Flow ◽

Data Flow Graph ◽

Commodity Flow ◽

Behavioral Synthesis ◽

Flow Problems ◽

Step Procedure

We propose an efficient binding algorithm for power optimization in behavioral synthesis. In prior work, it has been shown that several binding problems for low-power can be formulated as multi-commodity flow problems (due to an iterative execution of data flow graph) and be solved optimally. However, since the multi-commodity flow problem is NP-hard, the application is limited to a class of small sized problems. To overcome the limitation, we address the problem of how we can effectively make use of the property of efficient flow computations in a network so that it is extensively applicable to practical designs while producing close-to-optimal results. To this end, we propose a two-step procedure, which (1) determines a feasible binding solution by partially utilizing the computation steps for finding a maximum flow of minimum cost in a network and then (2) refines it iteratively. Experiments with a set of benchmark examples show that the proposed algorithm saves the run time significantly while maintaining close-to-optimal bindings in most practical designs.

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Networks Flow Applications

Graph Theory for Operations Research and Management ◽

10.4018/978-1-4666-2661-4.ch019 ◽

2013 ◽

pp. 246-256

Author(s):

Alireza Boloori ◽

Monirehalsadat Mahmoudi

Keyword(s):

Network Flow ◽

Large Scale ◽

Flow Problem ◽

Minimum Cost ◽

Maximum Flow ◽

Shortest Path Problems ◽

Flow Problems ◽

Large Scale Integration ◽

Minimum Cost Flow Problem ◽

Scale Integration

In this chapter, some applications of network flow problems are addressed based on each type of problem being discussed. For example, in the case of shortest path problems, their concept in facility layout, facility location, robotics, transportation, and very large-scale integration areas are pointed out in the first section. Furthermore, the second section deals with the implementation of the maximum flow problem in image segmentation, transportation, web communities, and wireless networks and telecommunication areas. Moreover, in the third section, the minimum-cost flow problem is discussed in fleeting and routing problems, petroleum, and scheduling areas. Meanwhile, a brief explanation about each application as well as some corresponding literature and research papers are presented in each section. In addition, based on available literature in each of these areas, some research gaps are identified, and future trends as well as chapter’s conclusion are pointed out in the fourth section.

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