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 two-edge 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 two-edge 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...

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 push-relabel 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.

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 trade-offs between a modular function and a submodular function can be found efficiently. We show results for speech recognition on the Switchboard-I 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

The identification of over-represented 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 ChIP-chip and geneexpression

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 Switchboard-I 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.

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 real-life examples.

Abstract. 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 Mumford-Shah 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 non-effectiveness 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