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17
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...
A PushRelabel Framework for Submodular Function Minimization and Applications to Parametric Optimization
 Discrete Applied Mathematics
, 2001
"... Recently, the first combinatorial strongly polynomial algorithms for submodular function minimization have been devised independently by Iwata, Fleischer, and Fujishige and by Schrijver. In this paper, we improve the running time of Schrijver's algorithm by designing a pushrelabel framework ..."
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Cited by 30 (6 self)
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Recently, the first combinatorial strongly polynomial algorithms for submodular function minimization have been devised independently by Iwata, Fleischer, and Fujishige and by Schrijver. In this paper, we improve the running time of Schrijver's algorithm by designing a pushrelabel framework for submodular function minimization (SFM). We also extend this algorithm to carry out parametric minimization for a strong map sequence of submodular functions in the same asymptotic running time as a single SFM. Applications include an eicient algorithm for finding a lexicographically optimal base.
Distributed algorithms for secure multipath routing in attackresistant networks,” Dept
 Comput. Sci
, 2007
"... Abstract—To proactively defend against intruders from readily jeopardizing singlepath data sessions, we propose a distributed secure multipath solution to route data across multiple paths so that intruders require much more resources to mount successful attacks. Our work exhibits several importan ..."
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Cited by 27 (1 self)
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Abstract—To proactively defend against intruders from readily jeopardizing singlepath data sessions, we propose a distributed secure multipath solution to route data across multiple paths so that intruders require much more resources to mount successful attacks. Our work exhibits several important properties that include: 1) routing decisions are made locally by network nodes without the centralized information of the entire network topology; 2) routing decisions minimize throughput loss under a singlelink attack with respect to different session models; and 3) routing decisions address multiple link attacks via lexicographic optimization. We devise two algorithms termed the BoundControl algorithm and the LexControl algorithm, both of which provide provably optimal solutions. Experiments show that the BoundControl algorithm is more effective to prevent the worstcase singlelink attack when compared to the singlepath approach, and that the LexControl algorithm further enhances the BoundControl algorithm by countering severe singlelink attacks and various types of multilink attacks. Moreover, the LexControl algorithm offers prominent protection after only a few execution rounds, implying that we can sacrifice minimal routing protection for significantly improved algorithm performance. Finally, we examine the applicability of our proposed algorithms in a specialized defensive network architecture called the attackresistant network and analyze how the algorithms address resiliency and security in different network settings. Index Terms—Attackresistant networks, maximumflow problems, multipath routing, optimization, preflowpush, resilience, security.
Optimal Selection of Limited Vocabulary Speech Corpora
"... We address the problem of finding a subset of a large speech data corpus that is useful for accurately and rapidly prototyping novel and computationally expensive speech recognition architectures. To solve this problem, we express it as an optimization problem over submodular functions. Quantities s ..."
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We address the problem of finding a subset of a large speech data corpus that is useful for accurately and rapidly prototyping novel and computationally expensive speech recognition architectures. To solve this problem, we express it as an optimization problem over submodular functions. Quantities such as vocabulary size (or quality) of a set of utterances, or quality of a bundle of word types are submodular functions which make finding the optimal solutions possible. We, moreover, are able to express our approach using graph cuts leading to a very fast implementation even on large initial corpora. We show results on the SwitchboardI corpus, demonstrating improved results over previous techniques for this purpose. We also demonstrate the variety of the resulting corpora that may be produced using our method. Index Terms: corpus subset selection, submodularity, LVCSR 1.
An application of the submodular principal partition to training data subset selection
 in NIPS Workshop on Discrete Optimization in Machine Learning: Submodularity, Sparsity & Polyhedra
, 2010
"... We address the problem of finding a subset of a large training data set (corpus) that is useful for accurately and rapidly prototyping novel and computationally expensive machine learning architectures. To solve this problem, we express it as an minimization problem over a weighted sum of modular fu ..."
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We address the problem of finding a subset of a large training data set (corpus) that is useful for accurately and rapidly prototyping novel and computationally expensive machine learning architectures. To solve this problem, we express it as an minimization problem over a weighted sum of modular functions and submodular functions. Quantities such as number of classes (or quality) in a set of samples, or quality of a bundle of classes are submodular functions which make finding the optimal solutions possible. We apply the principal partition to our problem such that solutions for all possible tradeoffs between a modular function and a submodular function can be found efficiently. We show results for speech recognition on the SwitchboardI speech recognition corpus, demonstrating improved results over previous techniques for this purpose. We also demonstrate the variety of the resulting corpora that may be produced using our method. 1
Finding Regulatory Motifs with Maximum Density Subgraphs
"... The identification of overrepresented but imperfectly conserved motifs in genomic DNA is a problem with important biological applications, such as the discovery of regulatory elements that determine the timing, location, and level of gene transcription. Experimental techniques such as ChIPchip and ..."
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The identification of overrepresented but imperfectly conserved motifs in genomic DNA is a problem with important biological applications, such as the discovery of regulatory elements that determine the timing, location, and level of gene transcription. Experimental techniques such as ChIPchip and geneexpression
Finding Dense Subgraphs for Sparse Undirected, Directed, and Bipartite Graphs
, 2009
"... This paper presents a method for identifying a set of dense subgraphs of a given sparse graph. Within the main applications of this “dense subgraph problem”, the dense subgraphs are interpreted as communities, as in, e.g., social networks. The problem of identifying dense subgraphs helps analyze gra ..."
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Cited by 1 (0 self)
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This paper presents a method for identifying a set of dense subgraphs of a given sparse graph. Within the main applications of this “dense subgraph problem”, the dense subgraphs are interpreted as communities, as in, e.g., social networks. The problem of identifying dense subgraphs helps analyze graph structures and complex networks and it is known to be challenging. It bears some similarities with the problem of reordering/blocking matrices in sparse matrix techniques. We exploit this link and adapt the idea of recognizing matrix column similarities, in order to compute a partial clustering of the vertices in a graph, where each cluster represents a dense subgraph. In contrast to existing subgraph extraction techniques which are based on a complete clustering of the graph nodes, the proposed algorithm takes into account the fact that not every participating node in the network needs to belong to a community. Another advantage is that the method does not require to specify the number of clusters; this number is usually not known in advance and is difficult to estimate. The computational process is very efficient, and the effectiveness of the proposed method is demonstrated in a few reallife examples.
Multilabel Markov Random Fields as an Efficient and Effective Tool for Image Segmentation, Total . . .
, 2012
"... One of the classical optimization models for image segmentation is the well known Markov Random Fields (MRF) model. This model is a discrete optimization problem, which is shown here to formulate many continuous models used in image segmentation, such as total variations, denoising, level sets and ..."
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One of the classical optimization models for image segmentation is the well known Markov Random Fields (MRF) model. This model is a discrete optimization problem, which is shown here to formulate many continuous models used in image segmentation, such as total variations, denoising, level sets and some classes of MumfordShah functionals. In spite of the presence of MRF in the literature, the dominant perception has been that the model is not effective for image segmentation. We show here that the reason for the noneffectiveness is not due to the power of the model. Rather it is due to the lack of access to the optimal solution. Instead of solving optimally, heuristics have been engaged. Those heuristic methods cannot guarantee the quality of the solution nor the running time of the algorithm. Worse still, heuristics do not link directly the input functions and parameters to the output thus obscuring what would be ideal choices of parameters and functions which are to be selected by users in each particular application context. In other cases, inefficient algorithms were used and therefore dismissed due to excessive computational requirements. We describe here how MRF can model and solve efficiently several known continuous
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)).