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A FASTER STRONGLY POLYNOMIAL MINIMUM COST FLOW ALGORITHM
, 1991
"... In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the EdmondsKarp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of O(n log n) shortest path problems on networks with n no ..."
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Cited by 116 (10 self)
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In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the EdmondsKarp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of O(n log n) shortest path problems on networks with n nodes and m arcs and runs in O(n log n (m + n log n)) time. Using a standard transformation, thjis approach yields an O(m log n (m + n log n)) algorithm for the capacitated minimum cost flow problem. This algorithm improves the best previous strongly polynomial time algorithm, due to Z. Galil and E. Tardos, by a factor of n 2 /m. Our algorithm for the capacitated minimum cost flow problem is even more efficient if the number of arcs with finite upper bounds, say n', is much less than m. In this case, the running time of the algorithm is O((m ' + n)log n(m + n log n)).
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 98 (7 self)
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. 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 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 theoretical work on related problems. Supported in part by ONR Young Investigator Award N0001491J1855, NSF Presidential Young Investigator Grant CCR8858097 with matching funds from AT&T and DEC, Stanford University Office of Technology Licensing, and a grant form the Powell Foundation. 1 1. Introduction. Significant theoretical progress has been made recently in the area of minimumcost flow ...
A Fast and Simple Algorithm for the Maximum Flow Problem
 OPERATIONS RESEARCH
, 1989
"... We present a simple sequential algorithm for the maximum flow problem on a network with n nodes, m arcs, and integer arc capacities bounded by U. Under the practical assumption that U is polynomially bounded in n, our algorithm runs in time O(nm + n 2 log n). This result improves the previous best b ..."
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Cited by 32 (6 self)
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We present a simple sequential algorithm for the maximum flow problem on a network with n nodes, m arcs, and integer arc capacities bounded by U. Under the practical assumption that U is polynomially bounded in n, our algorithm runs in time O(nm + n 2 log n). This result improves the previous best bound of O(nm log(n 2 /m)), obtained by Goldberg and Taran, by a factor of log n for networks that are both nonsparse and nondense without using any complex data structures. We also describe a parallel implementation of the algorithm that runs in O(n'log U log p) time in the PRAM model with EREW and uses only p processors where p = [m/n
DUAL COORDINATE STEP METHODS FOR LINEAR NETWORK FLOW PROBLEMS
, 1988
"... We review a class of recentlyproposed linearcost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of ecomplementary slackness, and most do not explicitly manipulate any "global " objects such as paths, trees, or cuts. Int ..."
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Cited by 31 (8 self)
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We review a class of recentlyproposed linearcost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of ecomplementary slackness, and most do not explicitly manipulate any "global " objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of new serial computational complexity results. We develop the basic theory of these methods and present two specific methods, the erelaxation algorithm for the minimumcost flow problem, and the auction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N 3 log NC) and O(NA log NC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implement erelaxation in a completely asynchronous, "chaotic" environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.
0/1Integer Programming: Optimization and Augmentation are Equivalent
 LECTURE NOTES IN COMPUTER SCIENCE, PROC. OF THE 3RD ANNUAL EUR. SYMPOS. ON ALGORITHMS
, 1995
"... For every family of sets F ` f0; 1g n the following problems are strongly polynomial time equivalent: given a feasible point x 0 2 F and a linear objective function c 2 ZZ n , ffl find a feasible point x 2 F that maximizes c x (Optimization), ffl find a feasible point x new 2 F with ..."
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Cited by 17 (6 self)
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For every family of sets F ` f0; 1g n the following problems are strongly polynomial time equivalent: given a feasible point x 0 2 F and a linear objective function c 2 ZZ n , ffl find a feasible point x 2 F that maximizes c x (Optimization), ffl find a feasible point x new 2 F with c x new ? c x 0 (Augmentation), and ffl find a feasible point x new 2 F with c x new ? c x 0 such that x new \Gamma x 0 is "irreducible" (Irreducible Augmentation). This generalizes results and techniques that are well known for 0=1 integer programming problems that arise from various classes of combinatorial optimization problems.
New DistanceDirected Algorithms for Maximum Flow and Parametric Maximum Flow Problems
, 1987
"... ..."
Distancedirected augmenting path algorithms for maximum flow and parametric maximum flow problems
 Naval Research Logistics
, 1991
"... Until recently, fast algorithms for the maximum flow problem have typically proceeded by constructing layered networks and establishing blocking flows in these networks. However, in recent years, new distancedirected algorithms have been suggested that do not construct layered networks but instead ..."
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Cited by 4 (1 self)
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Until recently, fast algorithms for the maximum flow problem have typically proceeded by constructing layered networks and establishing blocking flows in these networks. However, in recent years, new distancedirected algorithms have been suggested that do not construct layered networks but instead maintain a distance label with each node. The distance label of a node is a lower bound on the length of the shortest augmenting path from the node to the sink. In this article we develop two distancedirected augmenting path algorithms for the maximum flow problem. Both the algorithms run in O(n 2 m) time on networks with n nodes and m arcs. We also point out the relationship between the distance labels and layered networks. Using a scaling technique, we improve the complexity of our distancedirected algorithms to O(nm log U), where U denotes the largest arc capacity. We also consider applications of these algorithms to unit capacity maximum flow problems and a class of parametric maximum flow problems. t i
εRelaxations and Auction Methods for Separable Convex Cost Network Flow Problems
 In Network Optimization, Lecture Notes in Economics and Mathematical Systems
, 1996
"... We propose two new methods for the solution of the single commodity, separable convex cost network flow problem: the #relaxation method and the auction/sequential shortest path method. Both methods were originally developed for linear cost problems and reduce to their linear conterparts when applie ..."
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Cited by 2 (1 self)
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We propose two new methods for the solution of the single commodity, separable convex cost network flow problem: the #relaxation method and the auction/sequential shortest path method. Both methods were originally developed for linear cost problems and reduce to their linear conterparts when applied to such problems. We show that both methods stem from a common algorithmic framework, that they terminate with a near optimal solution, and we provide an associated complexity analysis. We also present computational results showing that these methods are much faster than earlier relaxation methods, particularly for illconditioned problems.