scholarly journals The Out-of-Kilter Algorithm and Its Applications to Network Flow Problems

2020 ◽  
pp. 76-97
Author(s):  
W. H. Moolman
Keyword(s):  
Network Flow ◽  
Network Flows ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Pascal Program ◽  
Complementary Slackness ◽  
Initial Flow ◽  
Shortest Path Problems ◽  
Flow Problems ◽  
Minimum Cost Flow Problem

The out-of-kilter algorithm, which was published by D.R. Fulkerson [1], is an algorithm that computes the solution to the minimum-cost flow problem in a flow network. To begin, the algorithm starts with an initial flow along the arcs and a number for each of the nodes in the network. By making use of Complementary Slackness Optimality Conditions (CSOC) [2], the algorithm searches for out-of-kilter arcs (those that do not satisfy CSOC conditions). If none are found the algorithm is complete. For arcs that do not satisfy the CSOC theorem, the flow needs to be increased or decreased to bring them into kilter. The algorithm will look for a path that either increases or decreases the flow according to the need. This is done until all arcs are in-kilter, at which point the algorithm is complete. If no paths are found to improve the system then there is no feasible flow. The Out-of-Kilter algorithm is applied to find the optimal solution to any problem that involves network flows. This includes problems such as transportation, assignment and shortest path problems. Computer solutions using a Pascal program and Matlab are demonstrated.

Networks Flow Applications

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.

scholarly journals Solving Robust Variants of Integer Flow Problems with Uncertain Arc Capacities

2021 ◽  
Vol 33 (1) ◽  
pp. 77-89
Author(s):  
Marko Špoljarec ◽  
Robert Manger
Keyword(s):  
Flow Problem ◽  
Network Flows ◽  
Minimum Cost ◽  
Maximum Flow ◽  
Approximate Algorithm ◽  
Minimum Cost Flow ◽  
Flow Problems ◽  
Unit Costs ◽  
Minimum Cost Flow Problem ◽  
Integer Flow

This paper deals with robust optimization and network flows. Several robust variants of integer flow problems are considered. They assume uncertainty of network arc capacities as well as of arc unit costs (where applicable). Uncertainty is expressed by discrete scenarios. Since the considered variants of the maximum flow problem are easy to solve, the paper is mostly concerned with NP-hard variants of the minimum-cost flow problem, thus proposing an approximate algorithm for their solution. The accuracy of the proposed algorithm is verified by experiments.

scholarly journals Adaptation of Random Binomial Graphs for Testing Network Flow Problems Algorithms

Mathematics ◽  
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.

Review of Network Flow Algorithms David P. Williamson

2021 ◽  
Vol 52 (1) ◽  
pp. 12-15
Author(s):  
S.V. Nagaraj
Keyword(s):  
Graduate Students ◽  
Real World ◽  
Network Flow ◽  
Network Flows ◽  
Optimization Problems ◽  
Capacity Constraints ◽  
Incoming Flow ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Real World Problems

This book is on algorithms for network flows. Network flow problems are optimization problems where given a flow network, the aim is to construct a flow that respects the capacity constraints of the edges of the network, so that incoming flow equals the outgoing flow for all vertices of the network except designated vertices known as the source and the sink. Network flow algorithms solve many real-world problems. This book is intended to serve graduate students and as a reference. The book is also available in eBook (ISBN 9781316952894/US$ 32.00), and hardback (ISBN 9781107185890/US$99.99) formats. The book has a companion web site www.networkflowalgs.com where a pre-publication version of the book can be downloaded gratis.

scholarly journals Minimum cost network flows: Problems, algorithms, and software

2013 ◽  
Vol 23 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Angelo Sifaleras
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Network Flows ◽  
Minimum Cost ◽  
Network Flow Problem ◽  
Software Packages ◽  
Wide Range ◽  
Solution Methods ◽  
Minimum Cost Network Flow ◽  
Algorithmic Approaches

We present a wide range of problems concerning minimum cost network flows, and give an overview of the classic linear single-commodity Minimum Cost Network Flow Problem (MCNFP) and some other closely related problems, either tractable or intractable. We also discuss state-of-the-art algorithmic approaches and recent advances in the solution methods for the MCNFP. Finally, optimization software packages for the MCNFP are presented.

Minimum cost time-varying network flow problems

2010 ◽  
Vol 25 (3) ◽  
pp. 429-447 ◽  
Author(s):  
Ebrahim Nasrabadi ◽  
S. Mehdi Hashemi
Keyword(s):  
Network Flow ◽  
Minimum Cost ◽  
Time Varying ◽  
Network Flow Problems ◽  
Flow Problems
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