scholarly journals Parallel Whale Optimization Algorithm for Maximum Flow Problem

2020 ◽  
Vol 14 (3) ◽  
pp. 30
Author(s):  
Raja Masadeh ◽  
Abdullah Alzaqebah ◽  
Bushra Smadi ◽  
Esra Masadeh
Keyword(s):  
Directed Graph ◽  
Optimization Algorithm ◽  
Flow Problem ◽  
Directed Graphs ◽  
Maximum Flow ◽  
Large Data ◽  
Maximum Flow Problem ◽  
Weighted Directed Graph ◽  
Long Run ◽  
Whale Optimization

Maximum Flow Problem (MFP) is considered as one of several famous problems in directed graphs. Many researchers studied MFP and its applications to solve problems using different techniques. One of the most popular algorithms that are employed to solve MFP is Ford-Fulkerson algorithm. However, this algorithm has long run time when it comes to application with large data size. For this reason, this study presents a parallel whale optimization (PWO) algorithm to get maximum flow in a weighted directed graph. The PWO algorithm is implemented and tested on datasets with different sizes. The PWO algorithm achieved up to 3.79 speedup on a machine with 4 processors.

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.

Complexity

1995 ◽  
Author(s):  
Raymond Greenlaw ◽  
H. James Hoover ◽  
Walter L. Ruzzo
Keyword(s):  
Directed Graph ◽  
Decision Problem ◽  
Flow Problem ◽  
Maximum Flow ◽  
The Other ◽  
Complexity Classes ◽  
Search Problem ◽  
Specific Question ◽  
Key Concepts ◽  
Formal Basis

The goal of this chapter is to provide the formal basis for many key concepts that are used throughout the book. These include the notions of problem, definitions of important complexity classes, reducibility, and completeness, among others. Thus far, we have used the term "problem" somewhat vaguely. In order to compare the difficulty of various problems we need to make this concept precise. Problems typically come in two flavors: search problems and decision problems. Consider the following search problem, to find the value of the maximum flow in a network. Example 3.1.1 Maximum Flow Value (MaxFlow-V) Given: A directed graph G = (V,E) with each edge e labeled by an integer capacity c(e) ≥ 0, and two distinguished vertices, s and t. Problem: Compute the value of the maximum flow from source s to sink t in G. The problem requires us to compute a number — the value of the maximum flow. Note, in this case we are actually computing a function. Now consider a variant of this problem. Example 3.1.2 Maximum Flow Bit (MaxFlow-B) Given: A directed graph G = (V, E) with each edge e labeled by an integer capacity c(e)≥ 0, and two distinguished vertices, s and t, and an integer i. Problem: Is the ith bit of the value of the maximum flow from source s to sink t in G a 1? This is a decision problem version of the flow problem. Rather than asking for the computation of some value, the problem is asking for a "yes" or "no" answer to a specific question. Yet the decision problem MaxFlow-B is equivalent to the search problem MaxFlow-V in the sense that if one can be solved efficiently in parallel, so can the other. Why is this? First consider how solving an instance of MaxFlow-B can be reduced to solving an instance of MaxFlow-V. Suppose that you are asked a question for MaxFlow-B, that is, "Is bit i of the maximum flow a 1?" It is easy to answer this question by solving MaxFlow-V and then looking at bit i of the flow.

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
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