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Mathematical Methods of Statistics
, 1946
"... Optimised flows and bottlenecks in granular fabric ..."
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Optimised flows and bottlenecks in granular fabric
A new approach to the maximum flow problem
 JOURNAL OF THE ACM
, 1988
"... All previously known efficient 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 pre ..."
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Cited by 642 (31 self)
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All previously known efficient 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(n³) 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(n²/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(n²log 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(n²) space.
An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1993
"... AbstractA novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated. The data to be clustered are represented by an undirected adjacency graph G with arc capacities assigned to reflect the similarity between the linked vert ..."
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AbstractA novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated. The data to be clustered are represented by an undirected adjacency graph G with arc capacities assigned to reflect the similarity between the linked vertices. Clustering is achieved by removing arcs of G to form mutually exclusive subgraphs such that the largest intersubgraph maximum flow is minimized. For graphs of moderate size ( 2000 vertices), the optimal solution is obtained through partitioning a flow and cut equivalent tree of 6, which can be efficiently constructed using the GomoryHu algorithm. However for larger graphs this approach is impractical. New theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size. This algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices. The new clustering algorithm is applied to the image segmentation problem. The segmentation is achieved by effectively searching for closed contours of edge elements (equivalent to minimum cuts in G), which consist mostly of strong edges, while rejecting contours containing isolated strong edges. This method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours. Index TermsClustering, edge contours, flow and cut equivalent tree, graph theory, image segmentation, subgraph condensation. D I.
Auction algorithms for network flow problems: A tutorial introduction
 Comput. Optim. Appl
, 1992
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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 46 (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...
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 44 (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...
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 32 (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.
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 31 (4 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