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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 134 (6 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 ...
Faster scaling algorithms for general graphmatching problems
 JOURNAL OF THE ACM
, 1991
"... An algorithm for minimumcost matching on a general graph with integral edge costs is presented. The algorithm runs in time close to the fastest known bound for maximumcardinality matching. Specifically, let n, m, and N denote the number of vertices, number of edges, and largest magnitude of a cost ..."
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Cited by 115 (3 self)
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An algorithm for minimumcost matching on a general graph with integral edge costs is presented. The algorithm runs in time close to the fastest known bound for maximumcardinality matching. Specifically, let n, m, and N denote the number of vertices, number of edges, and largest magnitude of a cost, respectively. The best known time bound for maximumcardinal ity matching M 0 ( Am). The new algorithm for minimumcost matching has time bound 0 ( in a ( m, n)Iog n m log ( nN)). A slight modification of the new algorithm finds a maximumcardinality matching in 0 ( fire) time. Other applications of the new algorlthm are given, mchrding an efficient implementation of Christofides ’ traveling salesman approximation algorithm and efficient solutions to update problems that require the linear programming duals for matching.
Auction algorithms for network flow problems: A tutorial introduction
 Comput. Optim. Appl
, 1992
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The auction algorithm: A distributed relaxation method for the assignment problem
, 1987
"... We propose a massively parallelizable algorithm for the classical assignment problem. The algorithm operates like an auction whereby unassigned persons bid simultaneously for objects thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. The algorithm can also ..."
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Cited by 101 (6 self)
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We propose a massively parallelizable algorithm for the classical assignment problem. The algorithm operates like an auction whereby unassigned persons bid simultaneously for objects thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. The algorithm can also be interpreted as a Jacobi like relaxation method for solving a dual problem. Its (sequential) worst case complexity, for a particular implementation that uses scaling, is O(NAlog(NC)) where N is the number of persons, A is the number of pairs of persons and objects that can be assigned to each other, and C is the maximum absolute object value. Computational results show that, for large problems, the algorithm is competitive with existing methods even without the benefit of parallelism. When executed on a parallel machine, the algorithm exhibits substantial speedup. * Work supported by Grant NSFECS8217668. Thanks are due to J. Kennington and L. Hatay of Southern Methodist Univ. for contributing some of their computational experience. Relaxation methods for optimal network flow problems resemble classical coordinate descent, Jacobi, and GaussSeidel methods for solving unconstrained nonlinear optimization
Improved Algorithms For Bipartite Network Flow
, 1994
"... In this paper, we study network flow algorithms for bipartite networks. A network G = (V; E) is called bipartite if its vertex set V can be partitioned into two subsets V 1 and V 2 such that all edges have one endpoint in V 1 and the other in V 2 . Let n = jV j, n 1 = jV 1 j, n 2 = jV 2 j, m = jE ..."
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Cited by 45 (4 self)
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In this paper, we study network flow algorithms for bipartite networks. A network G = (V; E) is called bipartite if its vertex set V can be partitioned into two subsets V 1 and V 2 such that all edges have one endpoint in V 1 and the other in V 2 . Let n = jV j, n 1 = jV 1 j, n 2 = jV 2 j, m = jEj and assume without loss of generality that n 1 n 2 . We call a bipartite network unbalanced if n 1 ø n 2 and balanced otherwise. (This notion is necessarily imprecise.) We show that several maximum flow algorithms can be substantially sped up when applied to unbalanced networks. The basic idea in these improvements is a twoedge push rule that allows us to "charge" most computation to vertices in V 1 , and hence develop algorithms whose running times depend on n 1 rather than n. For example, we show that the twoedge push version of Goldberg and Tarjan's FIFO preflow push algorithm runs in O(n 1 m + n 3 1 ) time and that the analogous version of Ahuja and Orlin's excess scaling algori...
THE AUCTION ALGORITHM FOR THE TRANSPORTATION PROBLEM
 ANNALS OF OPERATIONS RESEARCH 20(1989)6796 67
, 1989
"... The auction algorithm is a parallel relaxation nictliod for solving the classical assignment problem. It resembles a competitive bidding process whereby unussigncd persons bid simultaneously for objects, thereby raising their prices. Once all bids arc in, objects arc awarded to the highest bidder. T ..."
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Cited by 39 (3 self)
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The auction algorithm is a parallel relaxation nictliod for solving the classical assignment problem. It resembles a competitive bidding process whereby unussigncd persons bid simultaneously for objects, thereby raising their prices. Once all bids arc in, objects arc awarded to the highest bidder. Tliis paper generalizes the auction:ilgoritliin to solve linear transportation problems. The idea is to convert the transportation problem into an assignment problem, and then to inodily the auction algorithm to exploit the special structure of this problem. Computational results sliow Ihat this modified version of the auction algorithm is very efficient for certain types of transportation problems.
SublinearTime Parallel Algorithms for Matching and Related Problems
, 1988
"... This paper presents the first sublineartime deterministic parallel algorithms for bipartite matching and several related problems, including maximal nodedisjoint paths, depthfirst search, and flows in zeroone networks. Our results are based on a better understanding of the combinatorial struc ..."
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Cited by 36 (6 self)
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This paper presents the first sublineartime deterministic parallel algorithms for bipartite matching and several related problems, including maximal nodedisjoint paths, depthfirst search, and flows in zeroone networks. Our results are based on a better understanding of the combinatorial structure of the above problems, which leads to new algorithmic techniques. In particular, we show how to use maximal matching to extend, in parallel, a current set of nodedisjoint paths and how to take advantage of the parallelism that arises when a large number of nodes are "active" during an execution of a pushrelabel network flow algorithm. We also show how to apply our techniques to design parallel algorithms for the weighted versions of the above problems. In particular, we present sublineartime deterministic parallel algorithms for finding a minimumweight bipartite matching and for finding a minimumcost flow in a network with zeroone capacities, if the weights are polynomially ...
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 35 (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, and maximum arc cost magnitude C. The major techniques used are the capacityscaling approach of Edmonds and Karp, the excessscaling approach of Ahuja and Orlin, the costscaling approach of Goldberg and Tarjan, and the dynamic tree data structure of Sleator and Taijan. For nonsparse graphs with large maximum arc capacity, we obtain a similar but slightly better bound. We also obtain a slightly better bound for the (uncapacitated) transportation problem. In addition, we discuss a capacitybounding approach to the
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.