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Experimental evaluation of parametric maxflow algorithms
 In WEA ’07: Proceedings of the 6th Workshop on Experimental Algorithms
, 2007
"... 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 pushrelabel algorithm for ordinary maximum flow can ..."
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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 pushrelabel algorithm for ordinary maximum flow can be extended to the parametric problem while only increasing the worstcase 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 realworld 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. 1
Reflection methods for userfriendly submodular optimization
"... Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular functions, especially for minimization problems. While gener ..."
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Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular functions, especially for minimization problems. While general submodular minimization is challenging, we propose a new method that exploits existing decomposability of submodular functions. In contrast to previous approaches, our method is neither approximate, nor impractical, nor does it need any cumbersome parameter tuning. Moreover, it is easy to implement and parallelize. A key component of our method is a formulation of the discrete submodular minimization problem as a continuous best approximation problem that is solved through a sequence of reflections, and its solution can be easily thresholded to obtain an optimal discrete solution. This method solves both the continuous and discrete formulations of the problem, and therefore has applications in learning, inference, and reconstruction. In our experiments, we illustrate the benefits of our method on two image segmentation tasks. 1
ORACLEGUIDED SEARCH IN SORTED MATRICES IMPROVING BALANCED FLOW COMPUTATION
"... Abstract. In a successor search we are given a key x and a set A from a totally ordered universe and search for the smallest element of A that is larger than or equal to x. It is well known that the number of comparisons with x needed for this task changes from Θ(A) to Θ(log A) if A is stored in ..."
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Abstract. In a successor search we are given a key x and a set A from a totally ordered universe and search for the smallest element of A that is larger than or equal to x. It is well known that the number of comparisons with x needed for this task changes from Θ(A) to Θ(log A) if A is stored in sorted order. Here, we consider a related situation where the elements of A are organised as a so called sorted matrix. In such a matrix every column and every row is sorted. Further, x is given implicitly by a “monotone oracle”. Given a test value t, the oracle answers the question whether t ≥ x. We give a search algorithm for a sorted n × nmatrix performing O(log n) calls to the oracle and O(n) comparisons between matrix elements which we prove to be optimal. We extend this result to the case of nonsquare matrices and the situation where only columns are sorted. Our search techniques can be applied as the key tool to give an improved algorithm for the uniform balanced network flow problem (ubnfp). The ubnfp consists of finding a feasible stflow of given value F in a graph G = (V, A) which minimizes the difference of the maximum and the minimum flow on an arc. We show that our search techniques can be applied to obtain an O(log 2 m ·T 2 MF(n, m)) time algorithm for solving the ubnfp, where TMF(n, m) is the time required for a maximum flow computation in a network with n vertices and m arcs. This improves upon the previous best time bound of O(n 2 ·T 2 MF(n, m)).
Report 200813, July 2008ORACLEGUIDED SEARCH IN SORTED MATRICES IMPROVING BALANCED FLOW COMPUTATION
"... Oracleguided search in sorted matrices improving balanced flow compuatation ..."
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Oracleguided search in sorted matrices improving balanced flow compuatation
Activeset Methods for Submodular Optimization
, 2015
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.