scholarly journals A Review of Flow-Capacitated Networks: Algorithms, Techniques and Applications

2021 ◽  
pp. 1-33
Author(s):  
Omar Mutab Alsalami ◽  
Ali Muhammad Ali Rushdi
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Maximum Flow ◽  
Flow Properties ◽  
Transformation Techniques ◽  
Graph Theoretic ◽  
Network Problems ◽  
Definition Of ◽  
Capacitated Network ◽  
Alternative Solutions

This paper presents a review of flow network concepts, including definition of some graph-theoretic basics and a discussion of network flow properties. It also provides an overview of some crucial algorithms used to solve the maximum-flow problem such as the Ford and Fulkerson algorithm (FFA), supplemented with alternative solutions, together with the essential terminology for this algorithm. Moreover, this paper explains the max-flow min-cut theorem in detail, analyzes the concepts behind it, and provides some examples and their solutions to demonstrate this theorem. As a bonus, it expounds the reduction and transformation techniques used in a capacitated network. In addition, this paper reviews one of the popular techniques for analyzing capacitated networks, which is the “decomposition technique”. This technique is centered on conditioning a complicated network on the possible states of a keystone element  or on the possible combinations of states of many keystone elements. Some applications of capacitated network problems are addressed based on each type of problem being discussed.

scholarly journals Non-conserving Flow Aspect of Maximum Dynamic Flow Problem

2018 ◽  
Vol 14 (1) ◽  
pp. 107-114
Author(s):  
Phanindra Prasad Bhandari ◽  
Shree Ram Khadka
Keyword(s):  
Network Flow ◽  
Efficient Solution ◽  
Flow Problem ◽  
Dynamic Network ◽  
Maximum Flow ◽  
Solution Procedure ◽  
Evacuation Planning ◽  
Planning Problem ◽  
Intermediate Node ◽  
Flow Conservation

Shifting as many people as possible from disastrous area to safer area in a minimum time period in an efficient way is an evacuation planning problem (EPP). Modeling the evacuation scenarios reflecting the real world characteristics and investigation of an efficient solution to them have become a crucial due to rapidly increasing number of natural as well as human created disasters. EPPs modeled on network have been extensively studied and the various efficient solution procedures have been established where the flow function satisfies the flow conservation at each intermediate node. Besides this, the network flow problem in which flow may not be conserved at nodes necessarily could also be useful to model the evacuation planning problem. This paper proposes an efficient solution procedure for maximum flow evacuation planning problem of later kind on a single-source-single-sink dynamic network with integral arc capacities with holding capability of flow (evacuees) in the temporary shelter at intermediate nodes. Journal of the Institute of Engineering, 2018, 14(1): 107-114

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.

scholarly journals Playing with the Maximum-Flow Problem

10.29007/tkk1 ◽  
2018 ◽  
Author(s):  
Orna Kupferman
Keyword(s):  
Communication Networks ◽  
Flow Problem ◽  
Optimal Strategies ◽  
Maximum Flow ◽  
Computing Environment ◽  
Open Problems ◽  
Maximum Flow Problem ◽  
Road Systems ◽  
Definition Of ◽  
Special Case

In the traditional maximum-flow problem, the goal is to transfer maximum flow in a network by directing, in each vertex in the network, incoming flow into outgoing edges. The problem has been extensively used in order to optimize the performance of networks in numerous application areas. The definition of the problem corresponds to a setting in which the authority has control on all vertices of the network. Today’s computing environment involves parties that should be considered adversarial. We survey recent studies on flow games, which capture settings in which the vertices of the network are owned by different and selfish entities. We start with the case of two players, max (the authority), which aims at maximizing the flow, and min (the hostile environment), which aims at minimizing the flow. We argue that such flow games capture many modern settings, such as partially- controlled pipe or road systems or hybrid software-defined communication networks. We then continue to the special case where all vertices are owned by min. This case captures evacuation scenarios, where the goal is to maximize the flow that is guaranteed to travel in the most unfortunate routing decisions. Finally, we study the general case, of multiple players, each with her own target vertex. In all settings, we study the problems of finding the maximal flows, optimal strategies for the players, as well as stability and equilibrium inefficiency in the case of multi-player games. We discuss additional variants and their applications, and point to several interesting open problems.

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.

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.

A Combined Matheuristic for the Piecewise Linear Multicommodity Network Flow Problem

2017 ◽  
Vol 34 (06) ◽  
pp. 1750033 ◽  
Author(s):  
Naoto Katayama
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Piecewise Linear ◽  
Production Lines ◽  
Network Flow Problem ◽  
Multiple Resources ◽  
Network Problems ◽  
Local Branch ◽  
Multicommodity Network Flow ◽  
Communication Lines

Multicommodity network problems appear in numerous applications, such as telecommunications, logistics, transportation, distribution and production planning networks. The piecewise linear multicommodity network flow problem is a multicommodity network flow problem with piecewise linear costs corresponding to multiple resources, such as communication lines, vehicles and production lines. In the present paper, for the piecewise linear multicommodity network continuous flow problem, we present a path-based formulation and an arc-based formulation, and develop a combined matheuristic approach, which combines capacity scaling, a column and row generation technique, restricted branch-and-bound and a local branch method.

scholarly journals Graphs in Network Flows

2012 ◽  
Vol 11 (4) ◽  
pp. 99-108
Author(s):  
V Manjula
Keyword(s):  
Network Flow ◽  
Network Flows ◽  
Real Life ◽  
Maximum Flow ◽  
Modern World ◽  
Circuit Boards ◽  
Graph Theoretic ◽  
Life Problems ◽  
Theoretic Problem ◽  
Flow Of Information

This paper presents a collection of basics and application of Network flows in Graph theory which is an out- growth of set of lecture notes on Graph applications. It is not only a record of material from text books but also a reflection of precise graphical concept which will be useful for students where such facts are needed. There are many real life problems dealing with discrete objects and binary relations and graph is very convenient form of its representation. A network flow graph G=(V,E) is a directed graph with two special vertices: the source vertex s, and the sink vertex t. Many problems in the real world are to be solved using maximum flow. "Real" networks, like the Internet or electronic circuit boards, are good examples of flow networks. Generally graphs can be used in two situations. Firstly since graph is a very simple, convenient and natural way of representing the relationship between objects. Secondly we have graph as model solve the appropriate graph theoretic problem then interpret the solution in terms of original problem In the modern world, planning efficient routes is essential for business and industry, The flow of information or water or gas etc in a network are useful to find the max rate of flow that is possible from one station to another A Transport network represents a general model for transportation of material from origin of supply to destination through shipping routes. The objective of this paper is to discuss the concepts and terminology of Network flows with Graphical representations.

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.

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