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 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 Inverse Generalized Maximum Flow Problems

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 899 ◽  
Author(s):  
Javad Tayyebi ◽  
Adrian Deaconu
Keyword(s):  
Flow Problem ◽  
Natural Extension ◽  
Maximum Flow ◽  
Fast Method ◽  
Np Hard ◽  
Flow Problems ◽  
Maximum Flow Problem ◽  
Hard Problems ◽  
Optimum Solution ◽  
Np Hard Problems

A natural extension of maximum flow problems is called the generalized maximum flow problem taking into account the gain and loss factors for arcs. This paper investigates an inverse problem corresponding to this problem. It is to increase arc capacities as less cost as possible in a way that a prescribed flow becomes a maximum flow with respect to the modified capacities. The problem is referred to as the generalized maximum flow problem (IGMF). At first, we present a fast method that determines whether the problem is feasible or not. Then, we develop an algorithm to solve the problem under the max-type distances in O ( m n · log n ) time. Furthermore, we prove that the problem is strongly NP-hard under sum-type distances and propose a heuristic algorithm to find a near-optimum solution to these NP-hard problems. The computational experiments show the accuracy and the efficiency of the algorithm.

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.

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.

A Complexity Theoretic Parade of Network-Flow-Problems

1988 ◽  
Vol 11 (2) ◽  
pp. 195-208
Author(s):  
Christoph Meinel
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Complexity Classes ◽  
Network Flow Problems ◽  
Network Flow Problem ◽  
Flow Problems

In the following we prove the p-projection completeness of a number of extremely restricted modifications of the NETWORK-FLOW-PROBLEM for such well known nonuniform complexity classes like NC1, L, NL, co- NL, P, NP using a branching-program based characterization of these classes given in [Ba86] and [Me86a,b].

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 A combinatorial arc tolerance analysis for network flow problems

2005 ◽  
Vol 2005 (2) ◽  
pp. 83-94 ◽  
Author(s):  
P. T. Sokkalingam ◽  
Prabha Sharma
Keyword(s):  
Cost Function ◽  
Network Flow ◽  
Flow Problem ◽  
Tolerance Analysis ◽  
Network Flow Problems ◽  
Total Cost ◽  
Flow Problems ◽  
Optimal Flow ◽  
The Given ◽  
Total Cost Function

For the separable convex cost flow problem, we consider the problem of determining tolerance set for each arc cost function. For a given optimal flow x, a valid perturbation of cij(x) is a convex function that can be substituted for cij(x) in the total cost function without violating the optimality of x. Tolerance set for an arc(i,j) is the collection of all valid perturbations of cij(x). We characterize the tolerance set for each arc(i,j) in terms of nonsingleton shortest distances between nodes i and j. We also give an efficient algorithm to compute the nonsingleton shortest distances between all pairs of nodes in O(n3) time where n denotes the number of nodes in the given graph.

scholarly journals Two Flow Problems in Dynamic Networks

2016 ◽  
Vol 12 (1) ◽  
pp. 103 ◽  
Author(s):  
Camelia Schiopu ◽  
Eleonor Ciurea
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Flow Problem ◽  
Dynamic Networks ◽  
Maximum Flow ◽  
Flow Problems ◽  
Maximum Flow Problem

In this paper we study two flow problems: the feasible flow problem in dynamic networks and the maximum flow problem in bipartite dynamic networks with lower bounds. We mention that the maximum flow problem in bipartite dynamic networks with lower bound was presented in paper [8]a. For these problems we give examples.

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.

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