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 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.

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.

BINDING ALGORITHM FOR POWER OPTIMIZATION BASED ON NETWORK FLOW METHOD

2002 ◽  
Vol 11 (03) ◽  
pp. 259-271 ◽  
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.

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 Complexity Analysis of New Task Allocation Problem Using Network Flow Method on Multicore Clusters

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jixiang Yang
Keyword(s):  
Task Allocation ◽  
Network Flow ◽  
Flow Problem ◽  
Minimum Cost ◽  
Communication Cost ◽  
Minimum Cost Flow ◽  
Flow Method ◽  
Minimum Cost Flow Problem ◽  
Cost Flow ◽  
Multicore Clusters

The task allocation problem (TAP) generally aims to minimize total execution cost and internode communication cost in traditional parallel computing systems. New TAP (NTAP) considering additive intranode communication cost in emerging multicore cluster systems is investigated in this paper. We analyze the complexity of NTAP with network flow method and conclude that the intranode communication cost is a key to the complexity of NTAP, and prove that (1) the NTAP can be cast as a generalized linear network minimum cost flow problem and can be solved inO(m2n4)time if the intranode communication cost equals the internode communication cost, and (2) the NTAP can be cast as a generalized convex cost network minimum cost flow problem and can be solved in polynomial time if the intranode communication cost is more than the internode communication cost. More in particular, the uniform cost NTAP can be cast as a convex cost flow problem and can be solved inO(m2n2log(m+n))time. Furthermore, solutions to the NTAP are also discussed. Our work extends currently known theoretical results and the theorems and conclusions presented in this paper can provide theoretical basis for task allocating strategies on multicore clusters.

scholarly journals Power packet transferability via symbol propagation matrix

2018 ◽  
Vol 474 (2213) ◽  
pp. 20170552 ◽  
Author(s):  
Shinya Nawata ◽  
Atsuto Maki ◽  
Takashi Hikihara
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Temporal Structure ◽  
Minimum Cost ◽  
Finite Duration ◽  
Power Pulse ◽  
Minimum Cost Flow Problem ◽  
Propagation Matrix ◽  
Spatio Temporal ◽  
Symbol Sequences

A power packet is a unit of electric power composed of a power pulse and an information tag. In Shannon’s information theory, messages are represented by symbol sequences in a digitized manner. Referring to this formulation, we define symbols in power packetization as a minimum unit of power transferred by a tagged pulse. Here, power is digitized and quantized. In this paper, we consider packetized power in networks for a finite duration, giving symbols and their energies to the networks. A network structure is defined using a graph whose nodes represent routers, sources and destinations. First, we introduce the concept of a symbol propagation matrix (SPM) in which symbols are transferred at links during unit times. Packetized power is described as a network flow in a spatio-temporal structure. Then, we study the problem of selecting an SPM in terms of transferability, that is, the possibility to represent given energies at sources and destinations during the finite duration. To select an SPM, we consider a network flow problem of packetized power. The problem is formulated as an M-convex submodular flow problem which is a solvable generalization of the minimum cost flow problem. Finally, through examples, we verify that this formulation provides reasonable packetized power.

Transportation on Networks

2016 ◽  
Author(s):  
Alfred Galichon
Keyword(s):  
Shortest Path ◽  
Assignment Problem ◽  
Network Flow ◽  
Flow Problem ◽  
Optimal Assignment ◽  
Shortest Path Problems ◽  
Flow Problems ◽  
Optimal Flow ◽  
Optimal Network ◽  
The Difference

This chapter considers the optimal network flow problem, which is a generalization of the optimal assignment problem considered in Chapter 3. In optimal flow problems, one considers a network of cities, or edges, to move a distribution of mass on supply nodes to a distribution of mass on demand nodes. The difference from a standard optimal assignment problem is that the matching surplus associated with moving from a supply location to a demand location is not necessarily directly defined; instead, there are several paths from the supply location to the demand location, among these some yield maximal surplus. Therefore, both the optimal assignment problem and the shortest path problem are instances of the optimal flow problem; these instances are representative in the sense that any optimal flow problem may be decomposed into an assignment problem and a number of shortest path problems. The chapter shows how to easily compute these problems using linear programming.

scholarly journals Lexicographically Maximum Flows under an Arc Interdiction

2021 ◽  
Vol 4 (2) ◽  
pp. 8-14
Author(s):  
Phanindra Prasad Bhandari ◽  
Shree Ram Khadka
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Maximum Flow ◽  
Directed Network ◽  
Network System ◽  
Residual Flow ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Maximum Flow Problem ◽  
Maximum Flows

Network interdiction problem arises when an unwanted agent attacks the network system to deteriorate its transshipment efficiency. Literature is flourished with models and solution approaches for the problem. This paper considers a single commodity lexicographic maximum flow problem on a directed network with capacitated vertices to study two network flow problems under an arc interdiction. In the first, the objective is to find an arc on input network to be destroyed so that the residual lexicographically maximum flow is lexicographically minimum. The second problem aims to find a flow pattern resulting lexicographically maximum flow on the input network so that the total residual flow, if an arc is destroyed, is maximum. The paper proposes strongly polynomial time solution procedures for these problems.

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

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.

scholarly journals A Nonlinear Multiobjective Bilevel Model for Minimum Cost Network Flow Problem in a Large-Scale Construction Project

2012 ◽  
Vol 2012 ◽  
pp. 1-40 ◽  
Author(s):  
Jiuping Xu ◽  
Yan Tu ◽  
Ziqiang Zeng
Keyword(s):  
Network Flow ◽  
Large Scale ◽  
Simulated Annealing Algorithm ◽  
Flow Problem ◽  
Programming Model ◽  
Construction Project ◽  
Minimum Cost ◽  
Scale Construction ◽  
Network Flow Problem ◽  
Minimum Cost Network Flow

The aim of this study is to deal with a minimum cost network flow problem (MCNFP) in a large-scale construction project using a nonlinear multiobjective bilevel model with birandom variables. The main target of the upper level is to minimize both direct and transportation time costs. The target of the lower level is to minimize transportation costs. After an analysis of the birandom variables, an expectation multiobjective bilevel programming model with chance constraints is formulated to incorporate decision makers’ preferences. To solve the identified special conditions, an equivalent crisp model is proposed with an additional multiobjective bilevel particle swarm optimization (MOBLPSO) developed to solve the model. The Shuibuya Hydropower Project is used as a real-world example to verify the proposed approach. Results and analysis are presented to highlight the performances of the MOBLPSO, which is very effective and efficient compared to a genetic algorithm and a simulated annealing algorithm.

Sign in / Sign up

Export Citation Format

Share Document