Maximum common subgraph isomorphism algorithms for the matching of chemical structures

The maximum common subgraph (MCS) problem has become increasingly important in those aspects of chemoinformatics that involve the matching of 2D or 3D chemical structures. This paper provides a classification and a review of the many MCS algorithms, both exact and approximate, that have been described in the literature, and makes recommendations regarding their applicability to typical chemoinformatics tasks

Significant Subgraph Mining with Multiple Testing Correction

The problem of finding itemsets that are statistically significantly enriched in a class of transactions is complicated by the need to correct for multiple hypothesis testing. Pruning untestable hypotheses was recently proposed as a strategy for this task of significant itemset mining. It was shown to lead to greater statistical power, the discovery of more truly significant itemsets, than the standard Bonferroni correction on real-world datasets. An open question, however, is whether this strategy of excluding untestable hypotheses also leads to greater statistical power in subgraph mining, in which the number of hypotheses is much larger than in itemset mining. Here we answer this question by an empirical investigation on eight popular graph benchmark datasets. We propose a new efficient search strategy, which always returns the same solution as the state-of-the-art approach and is approximately two orders of magnitude faster. Moreover, we exploit the dependence between subgraphs by considering the effective number of tests and thereby further increase the statistical power.Comment: 18 pages, 5 figure, accepted to the 2015 SIAM International Conference on Data Mining (SDM15

Activity recognition from videos with parallel hypergraph matching on GPUs

In this paper, we propose a method for activity recognition from videos based on sparse local features and hypergraph matching. We benefit from special properties of the temporal domain in the data to derive a sequential and fast graph matching algorithm for GPUs. Traditionally, graphs and hypergraphs are frequently used to recognize complex and often non-rigid patterns in computer vision, either through graph matching or point-set matching with graphs. Most formulations resort to the minimization of a difficult discrete energy function mixing geometric or structural terms with data attached terms involving appearance features. Traditional methods solve this minimization problem approximately, for instance with spectral techniques. In this work, instead of solving the problem approximatively, the exact solution for the optimal assignment is calculated in parallel on GPUs. The graphical structure is simplified and regularized, which allows to derive an efficient recursive minimization algorithm. The algorithm distributes subproblems over the calculation units of a GPU, which solves them in parallel, allowing the system to run faster than real-time on medium-end GPUs

Solving Maximum Clique Problem for Protein Structure Similarity

A basic assumption of molecular biology is that proteins sharing close three-dimensional (3D) structures are likely to share a common function and in most cases derive from a same ancestor. Computing the similarity between two protein structures is therefore a crucial task and has been extensively investigated. Evaluating the similarity of two proteins can be done by finding an optimal one-to-one matching between their components, which is equivalent to identifying a maximum weighted clique in a specific "alignment graph". In this paper we present a new integer programming formulation for solving such clique problems. The model has been implemented using the ILOG CPLEX Callable Library. In addition, we designed a dedicated branch and bound algorithm for solving the maximum cardinality clique problem. Both approaches have been integrated in VAST (Vector Alignment Search Tool) - a software for aligning protein 3D structures largely used in NCBI (National Center for Biotechnology Information). The original VAST clique solver uses the well known Bron and Kerbosh algorithm (BK). Our computational results on real life protein alignment instances show that our branch and bound algorithm is up to 116 times faster than BK for the largest proteins