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20
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 155 (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 of problems for which all known methods seem to have almost quadratic time growth rate.
Experimental Study of Minimum Cut Algorithms
 PROCEEDINGS OF THE EIGHTH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA)
, 1997
"... Recently, several new algorithms have been developed for the minimum cut problem. These algorithms are very different from the earlier ones and from each other and substantially improve worstcase time bounds for the problem. We conduct experimental evaluation the relative performance of these algor ..."
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Cited by 40 (2 self)
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Recently, several new algorithms have been developed for the minimum cut problem. These algorithms are very different from the earlier ones and from each other and substantially improve worstcase time bounds for the problem. We conduct experimental evaluation the relative performance of these algorithms. In the process, we develop heuristics and data structures that substantially improve practical performance of the algorithms. We also develop problem families for testing minimum cut algorithms. Our work leads to a better understanding of practical performance of the minimum cut algorithms and produces very efficient codes for the problem.
An Efficient Cost Scaling Algorithm for the Assignment Problem
 MATH. PROGRAM
, 1995
"... The cost scaling pushrelabel method has been shown to be efficient for solving minimumcost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the ..."
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Cited by 36 (1 self)
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The cost scaling pushrelabel method has been shown to be efficient for solving minimumcost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the method is very promising for practical use.
Augment or Push? A computational study of Bipartite Matching and Unit Capacity Flow Algorithms
 ACM J. EXP. ALGORITHMICS
, 1998
"... We conduct a computational study of unit capacity flow and bipartite matching algorithms. Our goal is to determine which variant of the pushrelabel method is most efficient in practice and to compare pushrelabel algorithms with augmenting path algorithms. We have implemented and compared three pus ..."
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Cited by 30 (1 self)
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We conduct a computational study of unit capacity flow and bipartite matching algorithms. Our goal is to determine which variant of the pushrelabel method is most efficient in practice and to compare pushrelabel algorithms with augmenting path algorithms. We have implemented and compared three pushrelabel algorithms, three augmenting path algorithms (one of which is new), and one augmentrelabel algorithm. The depthfirst search augmenting path algorithm was thought to be a good choice for the bipartite matching problem, but our study shows that it is not robust. For the problems we study, our implementations of the fifo and lowestlevel selection pushrelabel algorithms have the most robust asymptotic rate of growth and work best overall. Augmenting path algorithms, although not as robust, on some problem classes are faster by a moderate constant factor. Our study includes several new problem families and input graphs with as many as 5 \Theta 10 5 vertices.
A Computational Study of the Pseudoflow and Pushrelabel Algorithms for the Maximum Flow Problem
"... We present the results of a computational investigation of the pseudoflow and pushrelabel algorithms for the maximum flow and minimum st cut problems. The two algorithms were tested on several problem instances from the literature. Our results show that our implementation of the pseudoflow algorit ..."
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Cited by 13 (5 self)
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We present the results of a computational investigation of the pseudoflow and pushrelabel algorithms for the maximum flow and minimum st cut problems. The two algorithms were tested on several problem instances from the literature. Our results show that our implementation of the pseudoflow algorithm is faster than the best known implementation of pushrelabel on most of the problem instances within our computational study. Subject classifications: Flow algorithms; parametric flow; normalized tree; lowest label; pseudoflow algorithm; maximum flow Area of review: Networks/graphs 1.
Global price updates help
, 1997
"... Periodic global updates of dual variables have been shown to yield a substantial speed advantage in implementations of pushrelabel algorithms for the maximum flow and minimum cost flow problems. In this paper, we show that in the context of the bipartite matching and assignment problems, global upd ..."
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Cited by 12 (4 self)
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Periodic global updates of dual variables have been shown to yield a substantial speed advantage in implementations of pushrelabel algorithms for the maximum flow and minimum cost flow problems. In this paper, we show that in the context of the bipartite matching and assignment problems, global updates yield a theoretical improvement as well. For bipartite matching, a pushrelabel algorithm that uses global updates runs in O ( √ log(n nm 2) /m) time (matching the best bound log n known) and performs worse by a factor of √ n without the updates. A similar result holds for the assignment problem, for which an algorithm that assumes integer costs in the range [ −C,...,C] and that runs in time O ( √ nm log(nC)) (matching the best costscaling bound known) is presented.
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 12 (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 distributed selfstabilizing algorithm for the maximum flow problem. Starting from an arbitrary state, the algorithm computes the maximum flow in a acyclic network in finitely many steps. Since the algorithm is selfstabilizing, it is inherently tolerant to transient faults and can automatically adjust to topology changes and to changes in other parameters of the problem. The paper presents extensive experimental results to indicate that the algorithm requires n 2 moves in an averagecase setting. A slight modification of the original algorithm is also presented and it is conjectured that the new algorithm computes a maximum flow in arbitrary networks. Key words. distributed algorithms, faulttoler...
Length Functions for Flow Computations
 NEC Research Institute
, 1997
"... We introduce a new approach to the maximum flow problem. This approach is based on assigning arc lengths based on the residual flow value and the residual arc capacities. Our approach leads to an O(min(n 2=3 ; m 1=2 )m log( n 2 m ) log U) time bound for a network with n vertices, m arcs, and ..."
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Cited by 11 (0 self)
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We introduce a new approach to the maximum flow problem. This approach is based on assigning arc lengths based on the residual flow value and the residual arc capacities. Our approach leads to an O(min(n 2=3 ; m 1=2 )m log( n 2 m ) log U) time bound for a network with n vertices, m arcs, and integral arc capacities in the range [1; : : : ; U ]. This is a fundamental improvement over the previous time bounds. We also improve bounds for the GomoryHu tree problem, the parametric flow problem, and the approximate st cut problems. 1 Introduction The maximum flow problem and its dual, the minimum cut problem, are classical combinatorial problems with a wide variety of scientific and engineering applications. The maximum flow problem and related flow and cut problems have been studied intensively for over three decades. The network simplex method of Dantzig [11] for the transportation problem, published in 1951, solves the maximum flow problem as a natural special case. Soon ther...
A Parallel CuttingPlane Algorithm for the Vehicle Routing Problem With Time Windows
, 1999
"... In the vehicle routing problem with time windows a number of identical vehicles must be routed to and from a depot to cover a given set of customers, each of whom has a specified time interval indicating when they are available for service. Each customer also has a known demand, and a vehicle may on ..."
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Cited by 11 (1 self)
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In the vehicle routing problem with time windows a number of identical vehicles must be routed to and from a depot to cover a given set of customers, each of whom has a specified time interval indicating when they are available for service. Each customer also has a known demand, and a vehicle may only serve the customers on a route if the total demand does not exceed the capacity of the vehicle. The most effective solution method proposed to date for this problem is due to Kohl, Desrosiers, Madsen, Solomon, and Soumis. Their algorithm uses a cuttingplane approach followed by a branchand bound search with column generation, where the columns of the LP relaxation represent routes of individual vehicles. We describe a new implementation of their method, using Karger's randomized minimumcut algorithm to generate cutting planes. The standard benchmark in this area is a set of 87 problem instances generated in 1984 by M. Solomon; making using of parallel processing in both the cuttingpla...