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A new approach to the maximum flow problem
 JOURNAL OF THE ACM
, 1988
"... All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the pre ..."
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Cited by 672 (34 self)
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All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based
On implementing the pushrelabel method for the maximum flow problem
, 1994
"... We study efficient implementations of the pushrelabel method for the maximum flow problem. The resulting codes are faster than the previous codes, and much faster on some problem families. The speedup is due to the combination of heuristics used in our implementation. We also exhibit a family of p ..."
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Cited by 208 (10 self)
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We study efficient implementations of the pushrelabel method for the maximum flow problem. The resulting codes are faster than the previous codes, and much faster on some problem families. The speedup is due to the combination of heuristics used in our implementation. We also exhibit a family
On the History of the Transportation and Maximum Flow Problems
"... We review two papers that are of historical interest for combinatorial optimization: an article of A.N. Tolstoi from 1930, in which the transportation problem is studied, and a negative cycle criterion is developed and applied to solve a (for that time) largescale (10 \Theta 68) transportation prob ..."
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Cited by 21 (0 self)
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problem to optimality; and an, until recently secret, RAND report of T.E. Harris and F.S. Ross from 1955, that Ford and Fulkerson mention as motivation to study the maximum flow problem. The papers have in common that they both apply their methods to the Soviet railway network.
The multiroute maximum flow problem revisited
, 2005
"... We are given a directed network G = (V, A, u) with vertex set V, arc set A, a source vertex s ∈ V, a destination vertex t ∈ V, a finite capacity vector u = {uij}ij∈A, and a positive integer m ∈ Z+. The multiroute maximum flow problem (mMFP) generalizes the ordinary maximum flow problem by seeking a ..."
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Cited by 2 (1 self)
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We are given a directed network G = (V, A, u) with vertex set V, arc set A, a source vertex s ∈ V, a destination vertex t ∈ V, a finite capacity vector u = {uij}ij∈A, and a positive integer m ∈ Z+. The multiroute maximum flow problem (mMFP) generalizes the ordinary maximum flow problem by seeking
The Maximum Flow Problem with Disjunctive Constraints
, 2010
"... We study the maximum flow problem subject to binary disjunctive constraints in a directed graph: A negative disjunctive constraint states that a certain pair of arcs in a digraph cannot be simultaneously used for sending flow in a feasible solution. In contrast to this, positive disjunctive constrai ..."
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We study the maximum flow problem subject to binary disjunctive constraints in a directed graph: A negative disjunctive constraint states that a certain pair of arcs in a digraph cannot be simultaneously used for sending flow in a feasible solution. In contrast to this, positive disjunctive
Rapidly Solving an Online Sequence of Maximum Flow Problems
, 2008
"... We investigate how to rapidly solve an online sequence of maximum flow problems. Sequences of maximum flow problems arise in a diverse collection of settings, including stochastic network programming and realtime scheduling of jobs on a twoprocessor computer. In this paper, we formulate solving an ..."
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Cited by 2 (2 self)
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We investigate how to rapidly solve an online sequence of maximum flow problems. Sequences of maximum flow problems arise in a diverse collection of settings, including stochastic network programming and realtime scheduling of jobs on a twoprocessor computer. In this paper, we formulate solving
Neural network models for solving the maximum flow problem
"... In this paper, two new neural network models for solving the maximum flow problem are presented. The maximum flow problem in networks is formulated as a special type of linear programming problem and it is solved by appropriately defined neural networks. The nonlinear neural networks are able to gen ..."
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In this paper, two new neural network models for solving the maximum flow problem are presented. The maximum flow problem in networks is formulated as a special type of linear programming problem and it is solved by appropriately defined neural networks. The nonlinear neural networks are able
TwoCommodity Multiroute Maximum Flow Problem
, 2005
"... We consider a twocommodity multiroute maximum flow problem in an undirected network— a generalization of the standard twocommodity maximum flow problem. An efficient combinatorial algorithm, which always guarantees a quarterinteger solution when the capacities are integers, is devised to solve a ..."
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We consider a twocommodity multiroute maximum flow problem in an undirected network— a generalization of the standard twocommodity maximum flow problem. An efficient combinatorial algorithm, which always guarantees a quarterinteger solution when the capacities are integers, is devised to solve a
A SelfStabilizing Algorithm For The Maximum Flow Problem
 Distributed Computing
, 1995
"... . The maximum flow problem is a fundamental problem in graph theory and combinatorial optimization with a variety of important applications. Known distributed algorithms for this problem do not tolerate faults or adjust to dynamic changes in network topology. This paper presents the first distribute ..."
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Cited by 14 (2 self)
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. The maximum flow problem is a fundamental problem in graph theory and combinatorial optimization with a variety of important applications. Known distributed algorithms for this problem do not tolerate faults or adjust to dynamic changes in network topology. This paper presents the first
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