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39
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 512 (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.
Applying parallel computation algorithms in the design of serial algorithms
 J. ACM
, 1983
"... Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for design ..."
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Cited by 234 (7 self)
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Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for designing an efficient serial algorithm for another problem. A d ~ eframework d for cases like this is presented. Particular cases, which are discussed in this paper, provide motivation for examining parallelism in sorting, selection, minimumspanningtree, shortest route, maxflow, and matrix multiplication problems, as well as in scheduling and locational problems.
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 151 (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.
A Simple LocalControl Approximation Algorithm for Multicommodity Flow
 In Proceedings of the 34th Annual Symposium on Foundations of Computer Science
, 1993
"... In this paper, we describe a very simple (1 + ") approximation algorithm for the multicommodity flow problem. The algorithm runs in time that is polynomial in N (the number of nodes in the network) and ffl \Gamma1 (the closeness of the approximation to optimal). The algorithm is remarkable in th ..."
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Cited by 65 (6 self)
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In this paper, we describe a very simple (1 + ") approximation algorithm for the multicommodity flow problem. The algorithm runs in time that is polynomial in N (the number of nodes in the network) and ffl \Gamma1 (the closeness of the approximation to optimal). The algorithm is remarkable in that it is much simpler than all known polynomial time flow algorithms (including algorithms for the special case of onecommodity flow). In particular, the algorithm does not rely on augmenting paths, shortest paths, mincost paths, or similar techniques to push flow through a network. In fact, no explicit attempt is ever made to push flow towards a sink during the algorithm. Because the algorithm is so simple, it can be applied to a variety of problems for which centralized decision making and flow planning is not possible. For example, the algorithm can be easily implemented with local control in a distributed network and it can be made tolerant to link failures. In addition, the algorithm ...
Scaling Algorithms for Network Problems
, 1985
"... This paper gives algorithms for network problems that work by scaling the numeric parameters. Assume all parameters are integers. Let n, m, and N denote the number of vertices, number of edges, and largest parameter of the network, respectively. A scaling algorithm for maximum weight matching on a b ..."
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Cited by 59 (2 self)
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This paper gives algorithms for network problems that work by scaling the numeric parameters. Assume all parameters are integers. Let n, m, and N denote the number of vertices, number of edges, and largest parameter of the network, respectively. A scaling algorithm for maximum weight matching on a bipartite graph runs in O(n3 % log N) time. For appropriate N this improves the traditional Hungarian method, whose most efftcient implementation is O(n(m + n log n)). The speedup results from finding augmenting paths in batches. The matching algorithm gives similar improvements for the following problems: singlesource shortest paths for arbitrary edge lengths (Bellman’s algorithm); maximum weight degreeconstrained subgraph; minimum cost flow on a cl network. Scaling gives a simple maximum value flow algorithm that matches the best known bound (Sleator and Tarjan’s algorithm) when log N = O(log n). Scaling also gives a good algorithm for shortest paths on a directed graph with nonnegative edge lengths (Dijkstra’s algorithm).
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 44 (7 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...
QOS Routing Via Multiple Paths Using Bandwidth Reservation
 In IEEE INFOCOM98: The Conference on Computer Communications
, 1998
"... vii 1 Introduction 1 1.1 Relation to Prior Work : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Contribution and Organization of the Paper : : : : : : : : : : : : : : 3 2 Problem Formulation 4 3 Message Transmission Problem 5 3.1 ShortestWidest Paths : : : : : : : : : : : : : : : : : : : ..."
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Cited by 39 (4 self)
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vii 1 Introduction 1 1.1 Relation to Prior Work : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Contribution and Organization of the Paper : : : : : : : : : : : : : : 3 2 Problem Formulation 4 3 Message Transmission Problem 5 3.1 ShortestWidest Paths : : : : : : : : : : : : : : : : : : : : : : : : : : 5 3.2 Properties of Multipaths : : : : : : : : : : : : : : : : : : : : : : : : : 6 3.3 NPCompleteness of MTP : : : : : : : : : : : : : : : : : : : : : : : : 10 3.4 Approximate Routing Algorithm : : : : : : : : : : : : : : : : : : : : 14 3.5 Relation to Maximum Flow Algorithm : : : : : : : : : : : : : : : : : 16 3.6 Simulation Results : : : : : : : : : : : : : : : : : : : : : : : : : : : : 18 3.7 DelayBandwidth Product : : : : : : : : : : : : : : : : : : : : : : : : 24 4 Sequence Transmission Problem 25 4.1 Intractability Results : : : : : : : : : : : : : : : : : : : : : : : : : : : 25 4.2 Approximation Algorithm : : : : : : : : : : : : : : : : : : : : : : : : 28 5 Concl...
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 34 (5 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