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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 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.
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 40 (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.
Augment or Push? A computational study of Bipartite Matching and Unit Capacity Flow Algorithms
 ACM J. EXP. ALGORITHMICS
, 1998
"... We conduct a computational study of unit capacity flow and bipartite matching algorithms. Our goal is to determine which variant of the pushrelabel method is most efficient in practice and to compare pushrelabel algorithms with augmenting path algorithms. We have implemented and compared three pus ..."
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Cited by 30 (1 self)
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We conduct a computational study of unit capacity flow and bipartite matching algorithms. Our goal is to determine which variant of the pushrelabel method is most efficient in practice and to compare pushrelabel algorithms with augmenting path algorithms. We have implemented and compared three pushrelabel algorithms, three augmenting path algorithms (one of which is new), and one augmentrelabel algorithm. The depthfirst search augmenting path algorithm was thought to be a good choice for the bipartite matching problem, but our study shows that it is not robust. For the problems we study, our implementations of the fifo and lowestlevel selection pushrelabel algorithms have the most robust asymptotic rate of growth and work best overall. Augmenting path algorithms, although not as robust, on some problem classes are faster by a moderate constant factor. Our study includes several new problem families and input graphs with as many as 5 \Theta 10 5 vertices.
A scalable graphcut algorithm for nd grids
 In Proceedings of CVPR
, 2008
"... Global optimisation via st graph cuts is widely used in computer vision and graphics. To obtain highresolution output, graph cut methods must construct massive ND gridgraphs containing billions of vertices. We show that when these graphs do not fit into physical memory, current maxflow/mincut ..."
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Cited by 23 (0 self)
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Global optimisation via st graph cuts is widely used in computer vision and graphics. To obtain highresolution output, graph cut methods must construct massive ND gridgraphs containing billions of vertices. We show that when these graphs do not fit into physical memory, current maxflow/mincut algorithms—the workhorse of graph cut methods—are totally impractical. Others have resorted to banded or hierarchical approximation methods that get trapped in local minima, which loses the main benefit of global optimisation. We enhance the pushrelabel algorithm for maximum flow [14] with two practical contributions. First, true global minima can now be computed on immense gridlike graphs too large for physical memory. These graphs are ubiquitous in computer vision, medical imaging and graphics. Second, for commodity multicore platforms our algorithm attains nearlinear speedup with respect to number of processors. To achieve these goals, we generalised the standard relabeling operations associated with pushrelabel. 1.
PARAMETRIC MAXIMUM FLOW ALGORITHMS FOR FAST TOTAL VARIATION MINIMIZATION
"... Abstract. This report studies the global minimization of discretized total variation (TV) energies with an L p (in particular, L 1 and L 2) fidelity term using parametric maximum flow algorithms to minimize st cut representations of these energies. The TV/L 2 model, also known as the RudinOsherFa ..."
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Cited by 20 (4 self)
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Abstract. This report studies the global minimization of discretized total variation (TV) energies with an L p (in particular, L 1 and L 2) fidelity term using parametric maximum flow algorithms to minimize st cut representations of these energies. The TV/L 2 model, also known as the RudinOsherFatemi (ROF) model is suitable for restoring images contaminated by Gaussian noise, while the TV/L 1 model is able to remove impulsive noise from greyscale images, and perform multiscale decompositions of them. Preliminary numerical results on largescale twodimensional CT and threedimensional Brain MR images are presented to illustrate the effectiveness of these approaches.
A Fast Approximation Scheme for Fractional Covering Problems with Box Constraints
, 2004
"... We present the first combinatorial approximation scheme that yields a pure approximation guarantee for linear programs that are either covering problems with upper bounds on variables, or their duals. Existing approximation schemes for mixed covering and packing problems do not simultaneously satis ..."
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Cited by 18 (2 self)
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We present the first combinatorial approximation scheme that yields a pure approximation guarantee for linear programs that are either covering problems with upper bounds on variables, or their duals. Existing approximation schemes for mixed covering and packing problems do not simultaneously satisfy packing and covering constraints exactly. We present the first combinatorial approximation scheme that returns solutions that simultaneously satisfy general positive covering constraints and upper bounds on variable values. For input parameter ffl? 0, the returned solution has positive linear objective function value at most 1 + ffl times the optimal value. The general algorithm requires O(ffl2m log(cTu)) iterations, where c is the objective cost vector, u is the vector of upper bound values, and m is the number of variables. Each iteration uses an oracle that finds an (approximately) most violated constraint. A natural set of problems that our work addresses are linear programs for various network design problems: generalized Steiner network, vertex connectivity, directed connectivity, capacitated network design, group Steiner forest. The integer versions of these problems are all NPhard. For each of them, there is an approximation algorithm that rounds the solution to the corresponding linear program relaxation. If the LP solution is not feasible, then the corresponding integer solution will also not be feasible. Solving the linear program is often the computational bottleneck in these problems, and thus a fast approximation scheme for the LP relaxation means faster approximation algorithms. For these applications, we introduce a new modification of the pushrelabel maximum flow algorithm that allows us to perform each iteration in amortized O(jEj+jV j log jV j) time, instead of one maximum flow per iteration that is implied by the straight forward adaptation of our general algorithm. In conjunction with an observation that reduces the number of iterations to jEj log jV j for f0; 1g constraint matrices, the modification allows us to obtain an algorithm that is faster than existing exact or approximate algorithms by a factor of at least O(jEj) and by a factor of O(jEj log jV j) if the number of demand pairs is \Omega (jV j).
What Do We Learn from Experimental Algorithmics?
 In Mathematical Foundations of Computer Science
, 2000
"... Experimental Algorithmics is concerned with the design, implementation, tuning, debugging and performance analysis of computer programs for solving algorithmic problems. It provides methodologies and tools for designing, developing and experimentally analyzing efficient algorithmic codes and aim ..."
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Cited by 6 (0 self)
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Experimental Algorithmics is concerned with the design, implementation, tuning, debugging and performance analysis of computer programs for solving algorithmic problems. It provides methodologies and tools for designing, developing and experimentally analyzing efficient algorithmic codes and aims at integrating and reinforcing traditional theoretical approaches for the design and analysis of algorithms and data structures. In this paper we survey some relevant contributions to the field of Experimental Algorithmics and we discuss significant examples where the experimental approach helped in developing new ideas, in assessing heuristics and techniques, and in gaining a deeper insight about existing algorithms. 1
Maximum flows by incremental breadthfirst search
 In ESA, LNCS 6942
, 2011
"... Abstract. Maximum flow and minimum st cut algorithms are used to solve several fundamental problems in computer vision. These problems have special structure, and standard techniques perform worse than the specialpurpose BoykovKolmogorov (BK) algorithm. We introduce the incremental breadthfirst ..."
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Cited by 5 (2 self)
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Abstract. Maximum flow and minimum st cut algorithms are used to solve several fundamental problems in computer vision. These problems have special structure, and standard techniques perform worse than the specialpurpose BoykovKolmogorov (BK) algorithm. We introduce the incremental breadthfirst search (IBFS) method, which uses ideas from BK but augments on shortest paths. IBFS is theoretically justified (runs in polynomial time) and usually outperforms BK on vision problems. 1
TwoLevel PushRelabel Algorithm for the Maximum Flow Problem
"... Abstract. We describe a twolevel pushrelabel algorithm for the maximum flow problem and compare it to the competing codes. The algorithm generalizes a practical algorithm for bipartite flows. Experiments show that the algorithm performs well on several problem families. 1 ..."
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Cited by 3 (1 self)
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Abstract. We describe a twolevel pushrelabel algorithm for the maximum flow problem and compare it to the competing codes. The algorithm generalizes a practical algorithm for bipartite flows. Experiments show that the algorithm performs well on several problem families. 1
Rice CAAM TR0709: a preliminary version Parametric Maximum Flow Algorithms for Fast Total Variation Minimization
, 2007
"... This report studies the global minimization of discretized total variation (TV) energies with an L 1 or L 2 fidelity term using parametric maximum flow algorithms. The TVL 2 model [36], also known as the RudinOsherFatemi (ROF) model is suitable for restoring images contaminated by Gaussian noise, ..."
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This report studies the global minimization of discretized total variation (TV) energies with an L 1 or L 2 fidelity term using parametric maximum flow algorithms. The TVL 2 model [36], also known as the RudinOsherFatemi (ROF) model is suitable for restoring images contaminated by Gaussian noise, while the TVL 1 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.