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Theoretical improvements in algorithmic efficiency for network flow problems

, 1972
"... This paper presents new algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimumcost flow problem. Upper bounds on ... the numbers of steps in these algorithms are derived, and are shown to compale favorably with upper bounds on the numbers of steps req ..."
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Cited by 560 (0 self)
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in the flow value then, provided the capacities are integral, a maximum flow will be determined within at most 1 + logM/(M1) if(t, S) augmentations, wheref*(t, s) is the value of the maximum flow and M is the maximum number of arcs across a cut. Next a new algorithm is given for the minimumcost flow
An Efficient Implementation Of A Scaling MinimumCost Flow Algorithm
 Journal of Algorithms
, 1992
"... . The scaling pushrelabel method is an important theoretical development in the area of minimumcost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve reallife performance of the method. Our implementation works very well o ..."
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Cited by 139 (6 self)
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over a wide range of problem classes. In our experiments, it was always competitive with the established codes, and usually outperformed these codes by a wide margin. Some heuristics we develop may apply to other network algorithms. Our experimental work on the minimumcost flow problem motivated
Finding MinimumCost Flows by Double Scaling
 MATHEMATICAL PROGRAMMING
, 1992
"... Several researchers have recently developed new techniques that give fast algorithms for the minimumcost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm log log U log(nC)) time on networks with n vertices, m arcs, maximum arc capacity U, and ..."
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Cited by 34 (7 self)
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Several researchers have recently developed new techniques that give fast algorithms for the minimumcost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm log log U log(nC)) time on networks with n vertices, m arcs, maximum arc capacity U
Approximate MinimumCost Multicommodity Flows In ... Time
, 1995
"... We show that an \epsilonapproximate solution of the costconstrained Kcommodity flow problem on an Nnode Marc network G can be computed by sequentially solving O(K(\epsilon^{2} log K) log M log(\epsilon^{1}K) singlecommodity minimumcost flow problems on the same network. In particular, an ap ..."
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Cited by 28 (0 self)
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We show that an \epsilonapproximate solution of the costconstrained Kcommodity flow problem on an Nnode Marc network G can be computed by sequentially solving O(K(\epsilon^{2} log K) log M log(\epsilon^{1}K) singlecommodity minimumcost flow problems on the same network. In particular
A Data Structure for Dynamic Trees
, 1983
"... A data structure is proposed to maintain a collection of vertexdisjoint trees under a sequence of two kinds of operations: a link operation that combines two trees into one by adding an edge, and a cut operation that divides one tree into two by deleting an edge. Each operation requires O(log n) ti ..."
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Cited by 347 (21 self)
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trees. (4) Implementing the network simplex algorithm for minimumcost flows. The most significant application is (2); an O(mn log n)time algorithm is obtained to find a maximum flow in a network of n vertices and m edges, beating by a factor of log n the fastest algorithm previously known for sparse
MINIMUMCOST FLOW PROBLEM AND APPLICATIONS IN NETWORKS
"... We consider the problem of finding the minimum cost of a feasible flow in directed networks. We allow realvalued upper bounds and convex and differentiable cost functions for the flows on arcs. In this paper, we present an efficient algorithm to solve such a large class of minimum cost flow problem ..."
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We consider the problem of finding the minimum cost of a feasible flow in directed networks. We allow realvalued upper bounds and convex and differentiable cost functions for the flows on arcs. In this paper, we present an efficient algorithm to solve such a large class of minimum cost flow
Approximating the MinimumCost Maximum Flow is PComplete
 Information Processing Letters
, 1992
"... We show that it is impossible, in NC, to approximate the value of the minimumcost maximum flow unless P = NC. Keywords: Theory of computation, Pcomplete, minimumcost flow, maximum flow. 1 Introduction Once a problem is proved to be Pcomplete, it is generally believed that there exists no NC or ..."
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Cited by 1 (0 self)
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maximum flow problem. We show that despite the fact that one can approximate the value of a maximum flow arbitrarily closely in RNC, approximating the value of the minimumcost maximum flow within a factor of C, the maximum cost in the network, is PComplete. Our proof also shows that this is true
Parallel Algorithms for the Assignment and MinimumCost Flow Problems
"... Let G = (V; E) be a network for an assignment problem with 2n nodes and m edges, in which the largest edge cost is C. Recently the class of instances of bipartite matching problems has been shown to be in RNC provided that C is O(log k n) for some fixed k. We show how to use scaling so as to dev ..."
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Cited by 3 (0 self)
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as to develop an improved parallel algorithm and show that bipartite matching problems are in the class RNC provided that C = O(n log k n ) for some fixed k. We then generalize these results to minimumcost flow problems. Let U be an upper bound on the capacities of the edges and on the largest demand. We
Results 1  10
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767