Mathematical Techniques for Efficient Record Segmentation in Large Shared Databases

Eisner, Mark; Severance, Dennis G.

doi:10.1145/321978.321982

Cited by 155 publications

(74 citation statements)

References 9 publications

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“…This key property is proved, at least for a particular case of submodular functions, in Gallo et al 1989, Lemma 2.4) (see also the references therein and in particular Eisner and Severance 1976). We also refer the reader to McCormick (1996) for further extensions of this approach.…”

Section: Lemma 34 Let Z > Z and θ θ Solve (8) For The Respective Vmentioning

confidence: 81%

“…It seems that efficiently solving the successive minimizations has been first proposed in the seminal work of Eisner and Severance (1976) in the context of augmenting-path maximumflow algorithms. It was then developed, analyzed and improved by Gallo et al (1989) for preflow-based algorithms.…”

Section: Quantized Total Variation Minimization Problemmentioning

confidence: 99%

“…Successive improvements were also proposed by Hochbaum (2001), specifically for the application in view in this paper, that is, the minimization of (15). We also refer to the work of Kolmogorov et al (2007) Following Eisner and Severance (1976), and assuming that one can perform exact floating point operations, one could solve (16) for all values of z. We will follow a different approach and introduce the following quantized version of Problem (15):…”

Section: Quantized Total Variation Minimization Problemmentioning

confidence: 99%

“…It is a very general approach, in the sense that if v − g 2 /2 is replaced with an arbitrary convex (C 1 , otherwise some (simple) adaption is required) potential i i (v i ), then (17) can be tackled in the same way with obvious modification (and this is, in general, optimal). However, for some "simple" potentials and in particular the one in (17), the method described in Eisner and Severance (1976), Gallo et al (1989), Hochbaum (2001) computes the exact solution (of course, in practice, up to machine precision) and is therefore optimal. We will return to this later on, when discussing the practical implementation, see Sect.…”

Section: Quantized Total Variation Minimization Problemmentioning

confidence: 99%

See 3 more Smart Citations

On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows

Chambolle

Darbon²

2009

Int J Comput Vis

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In a recent paper Boykov et al. (LNCS, Vol. 3953, pp. 409-422, 2006) propose an approach for computing curve and surface evolution using a variational approach and the geo-cuts method of Boykov and Kolmogorov (International conference on computer vision, pp. [26][27][28][29][30][31][32][33] 2003). We recall in this paper how this is related to well-known approaches for mean curvature motion, introduced by Alm-

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Section: Lemma 34 Let Z > Z and θ θ Solve (8) For The Respective Vmentioning

confidence: 81%

Section: Quantized Total Variation Minimization Problemmentioning

confidence: 99%

Section: Quantized Total Variation Minimization Problemmentioning

confidence: 99%

Section: Quantized Total Variation Minimization Problemmentioning

confidence: 99%

See 2 more Smart Citations

On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows

Chambolle

Darbon²

2009

Int J Comput Vis

147

183

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“…Applications of parametric maximum flow beyond those of ordinary maximum flow include product selection [3,12], database record segmentation [5], repair kit selection [11], and flow sharing [6].…”

Section: Introductionmentioning

confidence: 99%

Experimental Evaluation of Parametric Max-Flow Algorithms

Babenko

Derryberry

Goldberg

et al. 2007

Experimental Algorithms

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Abstract. The parametric maximum flow problem is an extension of the classical maximum flow problem in which the capacities of certain arcs are not fixed but are functions of a single parameter. Gallo et al. [6] showed that certain versions of the push-relabel algorithm for ordinary maximum flow can be extended to the parametric problem while only increasing the worst-case time bound by a constant factor. Recently Zhang et al. [14,13] proposed a novel, simple balancing algorithm for the parametric problem on bipartite networks. They claimed good performance for their algorithm on networks arising from a real-world application. We describe the results of an experimental study comparing the performance of the balancing algorithm, the GGT algorithm, and a simplified version of the GGT algorithm, on networks related to those of the application of Zhang et al. as well as networks designed to be hard for the balancing algorithm. Our implementation of the balancing algorithm beats both versions of the GGT algorithm on networks related to the application, thus supporting the observations of Zhang et al. On the other hand, the GGT algorithm is more robust; it beats the balancing algorithm on some natural networks, and by asymptotically increasing amount on networks designed to be hard for the balancing algorithm.

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Distance-directed augmenting path algorithms for maximum flow and parametric maximum flow problems

Ahuja

Orlin²

1991

Naval Research Logistics

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Until recently, fast algorithms for the maximum flow problem have typically proceeded by constructing layered networks and establishing blocking flows in these networks. However, in recent years, new distance‐directed algorithms have been suggested that do not construct layered networks but instead maintain a distance label with each node. The distance label of a node is a lower bound on the length of the shortest augmenting path from the node to the sink. In this article we develop two distance‐directed augmenting path algorithms for the maximum flow problem. Both the algorithms run in O(n2m) time on networks with n nodes and m arcs. We also point out the relationship between the distance labels and layered networks. Using a scaling technique, we improve the complexity of our distance‐directed algorithms to O(nm log U), where U denotes the largest arc capacity. We also consider applications of these algorithms to unit capacity maximum flow problems and a class of parametric maximum flow problems.

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Mathematical Techniques for Efficient Record Segmentation in Large Shared Databases

Cited by 155 publications

References 9 publications

On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows

On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows

Experimental Evaluation of Parametric Max-Flow Algorithms

Distance-directed augmenting path algorithms for maximum flow and parametric maximum flow problems

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