The max flow problem (original) (raw)

The maximum flow problem: a real-time approach

Parallel Computing, 2003

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An Innovative Approach for Solving Maximal-Flow Problems

This paper aims at introducing a new approach for finding the maximum flow of a maximal- flow problem requiring less number of iterations and less augmentation than Ford-Fulkerson algorithm. To illustrate the proposed method, a numerical example is presented. We have also formulated the maximal-flow problem as a linear programming problem (LPP) and solved it by using Bounded Variable Simplex Method.

An o(n3)o(n^3 )o(n3)-Time Maximum-Flow Algorithm

SIAM Journal on Computing, 1996

Das diesem Bericht zugrunde liegende Vorhaben wurde mit Mitteln des Bundesministers für Forschung und Technologie (Betreuungskennzeichen ITS 9103) gefördert. Die Verantwortung für den Inhalt dieser Veröffentlichung liegt beim Autor." An o(n 3)-Time Maximum-Flow Algorithm 1 ,2

Computational investigations of maximum flow algorithms

1997

Poznan, The maximum flow algorithm is distinguished by the long line of successive contributions researchers have made in ausanne, obtaining algorithms with ncrementally better worst-case complexity Some, but not all, of these theoretical improvements have produced improvements in practice. The purpose of this paper is to test some of the major algorithmic ideas developed in the recent years and to assess their utility on the empirical front. However, our study differs from previous studies in several ways. Whereas previous studies fcus primarily on CPU time analysis, our analysis goes further and provides naterials, detailed insight into algorithmic behavior. It not only observes how algorithms behave but also tries to explain why ,, Research recent algorithms that are likely to be efficient in practice. Our study encompasses ten maximum flow algorithms and five making, classes of networks. The augmenting path algorithms tested by us include Dinic's algorithm, the shortest augmenting path made for apable of algorithm, and the capacity-scaling algorithm. The preflow-push algorithms tested by us include Karzanov's algorithm, three apable of) :-Ant implementations of Goldberg-Tarjan's algorithm, and three versions of Ahuja-Orlin-Tarjan's excess-scaling algorithms. the past Among many findings, our study concludes that the preflow-push algorithms are substantially faster than other classes of nd of this nd of this algorithms, and the highest-label preflow-push algorithm is the fastest maximum flow algorithm for which the growth rate in structions i he editors structlons the computational time is O(n t ' 5) on four out of five of our problem classes. Further, in contrast to the results of the worst-case analysis of maximum flow algorithms, our study finds that the time to perform relabel operations (or constructing the layered networks) takes at least as much computation time as that taken by augmentations and/or pushes.

Improved Time Bounds for the Maximum Flow Problem

SIAM Journal on Computing, 1989

Recently, Goldberg proposed a new approach to the maximum network flow problem. The approach yields a very simple algorithm running in O(n 3) time on n-vertex networks. Incorporation of the dynamic tree data structure of Sleator and Tarjan yields a more complicated algorithm with a running time of O(nm log (n 2 /m)) on m-arc networks. Ahuja and Orlin developed a variant of Goldberg's algorithm that uses scaling and runs in O(nm + n 2 log U) time on networks with integer arc capacities bounded by U. In this paper possible improvements to the Ahuja-Orlin algorithm are explored. First, an improved running time of O(nnz + n log U/log log U) is obtained by using a nonconstant scaling factor. Second, an even better bound of O(nm + n2(log U) 1 /2) is obtained by combining the Ahuja-Orlin algorithm with the wave algorithm of Tarjan. Third, it is shown that the use of dynamic trees in the latter algorithm reduces the running time to O(nm log ((n/m)(log U)t/2 + 2)). This result shows that the combined use of three different techniques results in speed not obtained by using any of the techniques alone. The above bounds are all for a unit-cost random access machine. Also considered is a semilogarithmic computation model in which the bounds increase by an additive term of O(m log,, U), which is the time needed to read the input in the model.

Max flows in O(nm) time, or better

Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13, 2013

In this paper, we present improved polynomial time algorithms for the max flow problem defined on sparse networks with n nodes and m arcs. We show how to solve the max flow problem in O(nm + m 31/16 log 2 n) time. In the case that m = O(n 1.06 ), this improves upon the best previous algorithm due to King, Rao, and Tarjan, who solved the max flow problem in O(nm log m/(n log n) n) time. This establishes that the max flow problem is solvable in O(nm) time for all values of n and m. In the case that m = O(n), we improve the running time to O(n 2 / log n).

ON MAXIMUM FLOW OF NETWORKS

Zulfaqar J.Def. Eng. Tech, 2023

This paper aims to introduce and discuss two existing algorithms, namely Ford-Fulkerson's Algorithm and Dinic's Algorithm. These algorithms are for determining the maximum flow from source (s) to sink (t) in a flow network. A numerical example is solved to illustrate both algorithms, and to demonstrate, study, and compare the procedures at each iteration. The results show that Dinic's Algorithm returns the maximum flow that takes less number of iterations and augmentations than the Ford-Fulkerson Algorithm. In terms of complexity, the running time of Dinic's algorithm is (2), which should make it perform better on dense graphs. This goes to show that the claim by many researchers that Dinic's Algorithm is very powerful in solving big network flow problems is justified.

On multiroute maximum flows in networks

Networks, 2002

Let G = (N, A) be a network with a designated source node s, a designated sink node t, and a finite integral capacity ui 1 on each arc (i, j) E A. An elementary K-flow is a flow of K units from s to t such that the flow on each arc is 0 or 1. A K-route flow is a flow from s to t that may be expressed as a nonnegative linear sum of elementary K-flows. In this paper, we show how to determine a maximum K-route flow as a sequence of O(min {log (nU), K)) maximum-flow problems. This improves upon the algorithm by Kishimoto, which solves this problem as a sequence of K maximum-flow problems. In addition, we have simplified and extended some of the basic theory. We also discuss the application of our technique to Birkhoff's theorem and a scheduling problem.

Maximum Network Flow Algorithms

Journal of Advanced College of Engineering and Management

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.