64,824 research outputs found

    Comparison and improvement of algorithms for computing minimal cut sets

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    BACKGROUND: Constrained minimal cut sets (cMCSs) have recently been introduced as a framework to enumerate minimal genetic intervention strategies for targeted optimization of metabolic networks. Two different algorithmic schemes (adapted Berge algorithm and binary integer programming) have been proposed to compute cMCSs from elementary modes. However, in their original formulation both algorithms are not fully comparable. RESULTS: Here we show that by a small extension to the integer program both methods become equivalent. Furthermore, based on well-known preprocessing procedures for integer programming we present efficient preprocessing steps which can be used for both algorithms. We then benchmark the numerical performance of the algorithms in several realistic medium-scale metabolic models. The benchmark calculations reveal (i) that these preprocessing steps can lead to an enormous speed-up under both algorithms, and (ii) that the adapted Berge algorithm outperforms the binary integer approach. CONCLUSIONS: Generally, both of our new implementations are by at least one order of magnitude faster than other currently available implementations

    Tree-based Coarsening and Partitioning of Complex Networks

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    Many applications produce massive complex networks whose analysis would benefit from parallel processing. Parallel algorithms, in turn, often require a suitable network partition. For solving optimization tasks such as graph partitioning on large networks, multilevel methods are preferred in practice. Yet, complex networks pose challenges to established multilevel algorithms, in particular to their coarsening phase. One way to specify a (recursive) coarsening of a graph is to rate its edges and then contract the edges as prioritized by the rating. In this paper we (i) define weights for the edges of a network that express the edges' importance for connectivity, (ii) compute a minimum weight spanning tree TmT^m with respect to these weights, and (iii) rate the network edges based on the conductance values of TmT^m's fundamental cuts. To this end, we also (iv) develop the first optimal linear-time algorithm to compute the conductance values of \emph{all} fundamental cuts of a given spanning tree. We integrate the new edge rating into a leading multilevel graph partitioner and equip the latter with a new greedy postprocessing for optimizing the maximum communication volume (MCV). Experiments on bipartitioning frequently used benchmark networks show that the postprocessing already reduces MCV by 11.3%. Our new edge rating further reduces MCV by 10.3% compared to the previously best rating with the postprocessing in place for both ratings. In total, with a modest increase in running time, our new approach reduces the MCV of complex network partitions by 20.4%

    Incremental complexity of a bi-objective hypergraph transversal problem

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    The hypergraph transversal problem has been intensively studied, from both a theoretical and a practical point of view. In particular , its incremental complexity is known to be quasi-polynomial in general and polynomial for bounded hypergraphs. Recent applications in computational biology however require to solve a generalization of this problem, that we call bi-objective transversal problem. The instance is in this case composed of a pair of hypergraphs (A, B), and the aim is to find minimal sets which hit all the hyperedges of A while intersecting a minimal set of hyperedges of B. In this paper, we formalize this problem, link it to a problem on monotone boolean \land -- \lor formulae of depth 3 and study its incremental complexity

    Put three and three together: Triangle-driven community detection

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    Community detection has arisen as one of the most relevant topics in the field of graph data mining due to its applications in many fields such as biology, social networks, or network traffic analysis. Although the existing metrics used to quantify the quality of a community work well in general, under some circumstances, they fail at correctly capturing such notion. The main reason is that these metrics consider the internal community edges as a set, but ignore how these actually connect the vertices of the community. We propose the Weighted Community Clustering (WCC), which is a new community metric that takes the triangle instead of the edge as the minimal structural motif indicating the presence of a strong relation in a graph. We theoretically analyse WCC in depth and formally prove, by means of a set of properties, that the maximization of WCC guarantees communities with cohesion and structure. In addition, we propose Scalable Community Detection (SCD), a community detection algorithm based on WCC, which is designed to be fast and scalable on SMP machines, showing experimentally that WCC correctly captures the concept of community in social networks using real datasets. Finally, using ground-truth data, we show that SCD provides better quality than the best disjoint community detection algorithms of the state of the art while performing faster.Peer ReviewedPostprint (author's final draft

    Parallel Graph Partitioning for Complex Networks

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    Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel graph partitioners originally developed for more regular mesh-like networks do not work well for these networks. This paper addresses this problem by parallelizing and adapting the label propagation technique originally developed for graph clustering. By introducing size constraints, label propagation becomes applicable for both the coarsening and the refinement phase of multilevel graph partitioning. We obtain very high quality by applying a highly parallel evolutionary algorithm to the coarsened graph. The resulting system is both more scalable and achieves higher quality than state-of-the-art systems like ParMetis or PT-Scotch. For large complex networks the performance differences are very big. For example, our algorithm can partition a web graph with 3.3 billion edges in less than sixteen seconds using 512 cores of a high performance cluster while producing a high quality partition -- none of the competing systems can handle this graph on our system.Comment: Review article. Parallelization of our previous approach arXiv:1402.328
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