On the Complexity of Preflow-Push Algorithms for Maximum-Flow Problems I

Abstract. We study the maximum-flow algorithm of Goldberg and Tarjan and show that the largest-label implementation runs in O(nZxfm) time. We give a new proof of this fact. We compare our proof with the earlier work by Cheriyan and Maheswari who showed that the largest-label implementation of the preflow-push algorithm of Goldberg and Tarjan runs in O(n2x/~) time when implemented with current edges. Our proof that the number of nonsaturating pushes is O(n2x/m), does not rely on implementing pushes with current edges, therefore it is true for a much larger family of largest-label implementation of the preflow-push algorithms

Mathematical equivalence of the auction algorithm for assignment and the e-relaxation (preflow-push) method for min cost flow

Includes bibliographical references (p. 16-17).Supported by the NSF. CCR-9103804 Supported by the ARO. DAAL03-92-G-0115by Dimitri P. Bertsekas

A fast and simple algorithm for the maximum flow problem

Includes bibliographical references (p. 31-33)

Improved time bounds for the maximum flow problem

Also issued as: Working paper (Sloan School of Management) ; WP no. 1966-87Includes bibliographical references (p. 18-19).Research supported by the National Science Foundation. DCR-8605962 Research supported by the Office of Naval Research. NOOO14-87-K-0467by Ravindra K. Ahuja, James B. Orlin and Robert E. Tarjan

Diagnosing infeasibilities in network flow problems

"First Draft: June 13, 1994."Includes bibliographical references (p. 20-21).by Charu C. Aggarwal

A faster algorithm for finding the minimum cut in a graph

"December, 1992."Includes bibliographical references (p. 25-26).Jianxiu Hao and James B. Orlin

Graph-Informed Neural Networks for Regressions on Graph-Structured Data

In this work, we extend the formulation of the spatial-based graph convolutional networks with a new architecture, called the graph-informed neural network (GINN). This new architecture is specifically designed for regression tasks on graph-structured data that are not suitable for the well-known graph neural networks, such as the regression of functions with the domain and codomain defined on two sets of values for the vertices of a graph. In particular, we formulate a new graph-informed (GI) layer that exploits the adjacent matrix of a given graph to define the unit connections in the neural network architecture, describing a new convolution operation for inputs associated with the vertices of the graph. We study the new GINN models with respect to two maximum-flow test problems of stochastic flow networks. GINNs show very good regression abilities and interesting potentialities. Moreover, we conclude by describing a real-world application of the GINNs to a flux regression problem in underground networks of fractures

Um estudo do algoritmo de Goldberg e Tarjan para o problema de luxo maximo

Orientador: Clovis Perin FilhoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientíficaResumo: Este trabalho consiste no estudo e na implementação do algoritmo de Goldberg e Tarjan para o problema' do fluxo máximo. Este algoritmo tem destacada importância por apresentar uma das complexidades mais baixas e também pelo fato de abordar o problema de maneira diferenciada. Goldberg e Tarjan utilizam a estrutura de dados árvores dinâmicas para atingir a complexidade O(nm log(n2/m)) numa rede n-nós, m-arcos. Em redes densas (m = O (n2)) a complexidade deste algoritmo é tão boa quanto qualquer outro algoritmo, tendo uma das melhores complexidades em redes de densidade moderada. (m = O(n3/2)). Este algoritmo apresenta duas versões, uma que não utiliza a estrutura de dados árvores dinâmicas e tem complexidade O(n3), e outra versão que incorpora ao algoritmo anterior as árvores dinâmicas, conseguindo a complexidade de O(nm log(n2 1m)). Foram realizados testes comparativos com as duas versões e os principais al&oritmos conhecidos para o problema, tendo em vista o tempo de CPU em cada método. As redes utilizadas neste trabalho têm características particulares.Abstract: Not informed.MestradoMestre em Matemática Aplicad

Some Recent Advances in Network Flows

The literature on network flow problems is extensive, and over the past 40 years researchers have made continuous improvements to algorithms for solving several classes of problems. However, the surge of activity on the algorithmic aspects of network flow problems over the past few years has been particularly striking. Several techniques have proven to be very successful in permitting researchers to make these recent contributions: (i) scaling of the problem data; (ii) improved analysis of algorithms, especially amortized average case performance and the use of potential functions; and (iii) enhanced data structures. In this survey, we illustrate some of these techniques and their usefulness in developing faster network flow algorithms. Our discussion focuses on the design of faster algorithms from the worst case perspective and we limit our discussion to the following fundamental problems: the shortest path problem, the maximum flow problem, and the minimum cost flow problem. We consider several representative algorithms from each problem class including the radix heap algorithm for the shortest path problem, preflow push algorithms for the maximum flow problem, and the pseudoflow push algorithms for the minimum cost flow problem