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37
A new approach to the maximum flow problem
 Journal of the ACM
, 1988
"... Abstract. All previously known efftcient 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 ..."
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Cited by 506 (31 self)
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Abstract. All previously known efftcient 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 preflow concept of Karzanov is introduced. A preflow is like a flow, except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out. The method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths. The algorithm and its analysis are simple and intuitive, yet the algorithm runs as fast as any other known method on dense. graphs, achieving an O(n)) time bound on an nvertex graph. By incorporating the dynamic tree data structure of Sleator and Tarjan, we obtain a version of the algorithm running in O(nm log(n’/m)) time on an nvertex, medge graph. This is as fast as any known method for any graph density and faster on graphs of moderate density. The algorithm also admits efticient distributed and parallel implementations. A parallel implementation running in O(n’log n) time using n processors and O(m) space is obtained. This time bound matches that of the ShiloachVishkin algorithm, which also uses n processors but requires O(n’) space.
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 149 (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.
Faster scaling algorithms for network problems
 SIAM J. COMPUT
, 1989
"... This paper presents algorithms for the assignment problem, the transportation problem, and the minimumcost flow problem of operations research. The algorithms find a minimumcost solution, yet run in time close to the bestknown bounds for the corresponding problems without costs. For example, the ..."
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Cited by 125 (4 self)
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This paper presents algorithms for the assignment problem, the transportation problem, and the minimumcost flow problem of operations research. The algorithms find a minimumcost solution, yet run in time close to the bestknown bounds for the corresponding problems without costs. For example, the assignment problem (equivalently, minimumcost matching in a bipartite graph) can be solved in O(v/’rn log(nN)) time, where n, m, and N denote the number of vertices, number of edges, and largest magnitude of a cost; costs are assumed to be integral. The algorithms work by scaling. As in the work of Goldberg and Tarjan, in each scaled problem an approximate optimum solution is found, rather than an exact optimum.
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 99 (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 ...
Auction algorithms for network flow problems: A tutorial introduction
 Comput. Optim. Appl
, 1992
"... by ..."
Parallel SymmetryBreaking in Sparse Graphs
 SIAM J. Disc. Math
, 1987
"... We describe efficient deterministic techniques for breaking symmetry in parallel. These techniques work well on rooted trees and graphs of constant degree or genus. Our primary technique allows us to 3color a rooted tree in O(lg n) time on an EREW PRAM using a linear number of processors. We use th ..."
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Cited by 69 (2 self)
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We describe efficient deterministic techniques for breaking symmetry in parallel. These techniques work well on rooted trees and graphs of constant degree or genus. Our primary technique allows us to 3color a rooted tree in O(lg n) time on an EREW PRAM using a linear number of processors. We use these techniques to construct fast linear processor algorithms for several problems, including (\Delta + 1)coloring constantdegree graphs and 5coloring planar graphs. We also prove lower bounds for 2coloring directed lists and for finding maximal independent sets in arbitrary graphs. 1 Introduction Some problems for which trivial sequential algorithms exist appear to be much harder to solve in a parallel framework. When converting a sequential algorithm to a parallel one, at each step of the parallel algorithm we have to choose a set of operations which may be executed in parallel. Often, we have to choose these operations from a large set A preliminary version of this paper appear...
Scaling algorithms for the shortest paths problem
 In SODA ’93: Proceedings of the fourth annual ACMSIAM Symposium on Discrete algorithms
, 1993
"... Abstract. We describe a new method for designing scaling algorithms for the singlesource shortest paths problem and use this method to obtain an O (Vcfftn log N) algorithm for the problem. (Here n and m are the number of nodes and arcs in the input network and N is essentially the absolute value of ..."
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Cited by 56 (5 self)
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Abstract. We describe a new method for designing scaling algorithms for the singlesource shortest paths problem and use this method to obtain an O (Vcfftn log N) algorithm for the problem. (Here n and m are the number of nodes and arcs in the input network and N is essentially the absolute value of the most negative arc length; arc lengths are assumed to be integral.) This improves previous bounds for the problem. The method extends to related problems. Key words, shortest paths problem, graph theory, networks, scaling AMS subject classifications. 68Q20, 68Q25, 68R10, 05C70 1. Introduction. In
Computing Nash equilibria for scheduling on restricted parallel links
 In Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC
, 2004
"... We consider the problem of routing n users on m parallel links, under the restriction that each user may only be routed on a link from a certain set of allowed links for the user. Thus, the problem is equivalent to the correspondingly restricted problem of assigning n jobs to m parallel machines. In ..."
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Cited by 48 (9 self)
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We consider the problem of routing n users on m parallel links, under the restriction that each user may only be routed on a link from a certain set of allowed links for the user. Thus, the problem is equivalent to the correspondingly restricted problem of assigning n jobs to m parallel machines. In a pure Nash equilibrium, no user may improve its own individual cost (delay) by unilaterally switching to another link from its set of allowed links. As our main result, we introduce a polynomial time algorithm to compute from any given assignment a pure Nash equilibrium with nonincreased makespan. The algorithm gradually changes a given assignment by pushing unsplittable user traffics through a network that is defined by the users and the links. Here, we use ideas from blocking flows. Furthermore, we use similar techniques as in the generic PreflowPush algorithm to approximate a schedule with minimum makespan, gaining an improved approximation factor of 2 − 1 for identical links, where w1 is the largest user traffic. w1 We extend this result to related links, gaining an approximation factor of 2. Our approximation algorithms run in polynomial time. We close with tight upper bounds on the coordination ratio for pure Nash equilibria.
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 42 (6 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...