A maximum flow problem with intermediate node requirements

1983 ◽  
Vol 92 (3) ◽  
pp. 171-190
Author(s):  
S N Narahari Pandit ◽  
B Krishna Reddy
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Intermediate Node ◽  
Maximum Flow Problem

Efficiency of the Network Simplex Algorithm for the Maximum Flow Problem

1988 ◽  
Author(s):  
Andrew V. Goldberg ◽  
Michael D. Grigoriadis ◽  
Robert E. Tarjan
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Simplex Algorithm ◽  
Maximum Flow Problem ◽  
Network Simplex Algorithm ◽  
Network Simplex

Reverse maximum flow problem under the weighted Chebyshev distance

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1107-1121 ◽  
Author(s):  
Javad Tayyebi ◽  
Abumoslem Mohammadi ◽  
Seyyed Mohammad Reza Kazemi
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Binary Search ◽  
Second Phase ◽  
Sink Node ◽  
Search Technique ◽  
Bound Constraints ◽  
Maximum Flow Problem ◽  
Optimal Value ◽  
Two Phases

Given a network G(V, A, u) with two specific nodes, a source node s and a sink node t, the reverse maximum flow problem is to increase the capacity of some arcs (i, j) as little as possible under bound constraints on the modifications so that the maximum flow value from s to t in the modified network is lower bounded by a prescribed value v0. In this paper, we study the reverse maximum flow problem when the capacity modifications are measured by the weighted Chebyshev distance. We present an efficient algorithm to solve the problem in two phases. The first phase applies the binary search technique to find an interval containing the optimal value. The second phase uses the discrete type Newton method to obtain exactly the optimal value. Finally, some computational experiments are conducted to observe the performance of the proposed algorithm.

scholarly journals Engineering Bi-Connected Component Overlay for Maximum-Flow Parallel Acceleration in Large Sparse Graph

2018 ◽  
Vol 36 (5) ◽  
pp. 955-962
Author(s):  
Yang Liu ◽  
Wei Wei ◽  
Heyang Xu
Keyword(s):  
Large Scale ◽  
Flow Problem ◽  
Maximum Flow ◽  
Low Complexity ◽  
Connected Components ◽  
Sparse Graphs ◽  
Fully Integrated ◽  
Flow Acceleration ◽  
Maximum Flow Problem ◽  
Graph Contraction

Network maximum flow problem is important and basic in graph theory, and one of its research directions is maximum-flow acceleration in large-scale graph. Existing acceleration strategy includes graph contraction and parallel computation, where there is still room for improvement:(1) The existing two acceleration strategies are not fully integrated, leading to their limited acceleration effect; (2) There is no sufficient support for computing multiple maximum-flow in one graph, leading to a lot of redundant computation. (3)The existing preprocessing methods need to consider node degrees and capacity constraints, resulting in high computational complexity. To address above problems, we identify the bi-connected components in a given graph and build an overlay, which can help split the maximum-flow problem into several subproblems and then solve them in parallel. The algorithm only uses the connectivity in the graph and has low complexity. The analyses and experiments on benchmark graphs indicate that the method can significantly shorten the calculation time in large sparse graphs.

A Distributed Preflow-Push for the Maximum Flow Problem

2006 ◽  
pp. 195-206 ◽  
Author(s):  
Thuy Lien Pham ◽  
Marc Bui ◽  
Ivan Lavallee ◽  
Si Hoang Do
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Maximum Flow Problem

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

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