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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 158 (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.
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 43 (5 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...
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 41 (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.
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 32 (6 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
A Faster Algorithm for Finding the Minimum Cut in a Directed Graph
 JOURNAL OF ALGORITHMS
, 1994
"... We consider the problem of finding the minimum capacity cut in a directed network G with n nodes. This problem has applications to network reliability and survivability and is useful in subroutines for other network optimization problems. One can use a maximum flow problem to find a minimum cut sepa ..."
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Cited by 32 (0 self)
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We consider the problem of finding the minimum capacity cut in a directed network G with n nodes. This problem has applications to network reliability and survivability and is useful in subroutines for other network optimization problems. One can use a maximum flow problem to find a minimum cut separating a designated source node s from a designated sink node t, and by varying the sink node one can find a minimum cut in G as a sequence of at most 2n 2 maximum flow problems. We then show how to reduce the running time of these 2n 2 maximum flow algorithms to the running time for solving a single maximum flow problem. The resulting running time is O(nm log(n 2 /m)) for finding the minimum cut in either a directed or an undirected network. © 1994 Academic Press, Inc. 1.
Parametric Maximum Flow Algorithms for Fast Total Variation Minimization
, 2007
"... This report studies the global minimization of discretized total variation (TV) energies with an L¹ or L² fidelity term using parametric maximum flow algorithms. The TVL² model [36], also known as the RudinOsherFatemi (ROF) model is suitable for restoring images contaminated by Gaussian noise, wh ..."
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Cited by 22 (4 self)
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This report studies the global minimization of discretized total variation (TV) energies with an L¹ or L² fidelity term using parametric maximum flow algorithms. The TVL² model [36], also known as the RudinOsherFatemi (ROF) model is suitable for restoring images contaminated by Gaussian noise, while the TVL¹ model [2, 29, 7, 42] is able to remove impulsive noise from greyscale images, and perform multi scale decompositions of them. For largescale applications such as those in medical image (pre)processing, we propose here fast and memoryefficient algorithms, based on a parametric maximum flow algorithm [19] and the minimum st cut representation of TVbased energy functions [26, 17]. Preliminary numerical results on largescale twodimensional CT and threedimensional Brain MRI images that illustrate the effectiveness of our approaches are presented.
On Implementing Graph Cuts on CUDA
"... has enabled graphics processors to be explicitly programmed as generalpurpose sharedmemory multicore processors with a high level of parallelism. In this paper, we present our preliminary results of implementing the Graph Cuts algorithm on CUDA. Our primary focus is on implementing Graph Cuts on ..."
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Cited by 14 (1 self)
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has enabled graphics processors to be explicitly programmed as generalpurpose sharedmemory multicore processors with a high level of parallelism. In this paper, we present our preliminary results of implementing the Graph Cuts algorithm on CUDA. Our primary focus is on implementing Graph Cuts on grid graphs, which are extensively used in imaging applications. We first explain our implementation of breadth first search (BFS) graph traversal on CUDA, which is extensively used in our Graph Cuts implementation. We then present a basic implementation of Graph Cuts that succeeds to achieve absolute and relative speedups when used for foregroundbackground segmentation on synthesized images. Finally, we introduce two optimizations that utilize the special structure of grid graphs. The first one is lockstep BFS, which is used to reduce the overhead of BFS traversals. The second is cache emulation, which is a general technique to regularize memory access patterns and hence enhance memory access throughput. We experimentally show how each of the two optimizations can enhance the performance of the basic implementation on the image segmentation application. I.