RASCAL: calculation of graph similarity using maximum common edge subgraphs

A new graph similarity calculation procedure is introduced for comparing labeled graphs. Given a minimum similarity threshold, the procedure consists of an initial screening process to determine whether it is possible for the measure of similarity between the two graphs to exceed the minimum threshold, followed by a rigorous maximum common edge subgraph (MCES) detection algorithm to compute the exact degree and composition of similarity. The proposed MCES algorithm is based on a maximum clique formulation of the problem and is a significant improvement over other published algorithms. It presents new approaches to both lower and upper bounding as well as vertex selection

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

Structural matching by discrete relaxation

This paper describes a Bayesian framework for performing relational graph matching by discrete relaxation. Our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching. Broadly speaking there are two main aspects to this study. Firstly we locus on the issue of how relational inexactness may be quantified. We illustrate that several popular relational distance measures can be recovered as specific limiting cases of the Bayesian consistency measure. The second aspect of our comparison concerns the way in which structural inexactness is controlled. We investigate three different realizations ai the matching process which draw on contrasting control models. The main conclusion of our study is that the active process of graph-editing outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter

A graph theoretic approach to scene matching

The ability to match two scenes is a fundamental requirement in a variety of computer vision tasks. A graph theoretic approach to inexact scene matching is presented which is useful in dealing with problems due to imperfect image segmentation. A scene is described by a set of graphs, with nodes representing objects and arcs representing relationships between objects. Each node has a set of values representing the relations between pairs of objects, such as angle, adjacency, or distance. With this method of scene representation, the task in scene matching is to match two sets of graphs. Because of segmentation errors, variations in camera angle, illumination, and other conditions, an exact match between the sets of observed and stored graphs is usually not possible. In the developed approach, the problem is represented as an association graph, in which each node represents a possible mapping of an observed region to a stored object, and each arc represents the compatibility of two mappings. Nodes and arcs have weights indicating the merit or a region-object mapping and the degree of compatibility between two mappings. A match between the two graphs corresponds to a clique, or fully connected subgraph, in the association graph. The task is to find the clique that represents the best match. Fuzzy relaxation is used to update the node weights using the contextual information contained in the arcs and neighboring nodes. This simplifies the evaluation of cliques. A method of handling oversegmentation and undersegmentation problems is also presented. The approach is tested with a set of realistic images which exhibit many types of sementation errors

A lightweight, graph-theoretic model of class-based similarity to support object-oriented code reuse.

The work presented in this thesis is principally concerned with the development of a method and set of tools designed to support the identification of class-based similarity in collections of object-oriented code. Attention is focused on enhancing the potential for software reuse in situations where a reuse process is either absent or informal, and the characteristics of the organisation are unsuitable, or resources unavailable, to promote and sustain a systematic approach to reuse. The approach builds on the definition of a formal, attributed, relational model that captures the inherent structure of class-based, object-oriented code. Based on code-level analysis, it relies solely on the structural characteristics of the code and the peculiarly object-oriented features of the class as an organising principle: classes, those entities comprising a class, and the intra and inter-class relationships existing between them, are significant factors in defining a two-phase similarity measure as a basis for the comparison process. Established graph-theoretic techniques are adapted and applied via this model to the problem of determining similarity between classes. This thesis illustrates a successful transfer of techniques from the domains of molecular chemistry and computer vision. Both domains provide an existing template for the analysis and comparison of structures as graphs. The inspiration for representing classes as attributed relational graphs, and the application of graph-theoretic techniques and algorithms to their comparison, arose out of a well-founded intuition that a common basis in graph-theory was sufficient to enable a reasonable transfer of these techniques to the problem of determining similarity in object-oriented code. The practical application of this work relates to the identification and indexing of instances of recurring, class-based, common structure present in established and evolving collections of object-oriented code. A classification so generated additionally provides a framework for class-based matching over an existing code-base, both from the perspective of newly introduced classes, and search "templates" provided by those incomplete, iteratively constructed and refined classes associated with current and on-going development. The tools and techniques developed here provide support for enabling and improving shared awareness of reuse opportunity, based on analysing structural similarity in past and ongoing development, tools and techniques that can in turn be seen as part of a process of domain analysis, capable of stimulating the evolution of a systematic reuse ethic

Fine-grained Search Space Classification for Hard Enumeration Variants of Subset Problems

We propose a simple, powerful, and flexible machine learning framework for (i) reducing the search space of computationally difficult enumeration variants of subset problems and (ii) augmenting existing state-of-the-art solvers with informative cues arising from the input distribution. We instantiate our framework for the problem of listing all maximum cliques in a graph, a central problem in network analysis, data mining, and computational biology. We demonstrate the practicality of our approach on real-world networks with millions of vertices and edges by not only retaining all optimal solutions, but also aggressively pruning the input instance size resulting in several fold speedups of state-of-the-art algorithms. Finally, we explore the limits of scalability and robustness of our proposed framework, suggesting that supervised learning is viable for tackling NP-hard problems in practice.Comment: AAAI 201

Binding site matching in rational drug design: Algorithms and applications

© 2018 The Author(s) 2018. Published by Oxford University Press. All rights reserved. Interactions between proteins and small molecules are critical for biological functions. These interactions often occur in small cavities within protein structures, known as ligand-binding pockets. Understanding the physicochemical qualities of binding pockets is essential to improve not only our basic knowledge of biological systems, but also drug development procedures. In order to quantify similarities among pockets in terms of their geometries and chemical properties, either bound ligands can be compared to one another or binding sites can be matched directly. Both perspectives routinely take advantage of computational methods including various techniques to represent and compare small molecules as well as local protein structures. In this review, we survey 12 tools widely used to match pockets. These methods are divided into five categories based on the algorithm implemented to construct binding-site alignments. In addition to the comprehensive analysis of their algorithms, test sets and the performance of each method are described. We also discuss general pharmacological applications of computational pocket matching in drug repurposing, polypharmacology and side effects. Reflecting on the importance of these techniques in drug discovery, in the end, we elaborate on the development of more accurate meta-predictors, the incorporation of protein flexibility and the integration of powerful artificial intelligence technologies such as deep learning

Graph theoretic methods for the analysis of structural relationships in biological macromolecules

Subgraph isomorphism and maximum common subgraph isomorphism algorithms from graph theory provide an effective and an efficient way of identifying structural relationships between biological macromolecules. They thus provide a natural complement to the pattern matching algorithms that are used in bioinformatics to identify sequence relationships. Examples are provided of the use of graph theory to analyze proteins for which three-dimensional crystallographic or NMR structures are available, focusing on the use of the Bron-Kerbosch clique detection algorithm to identify common folding motifs and of the Ullmann subgraph isomorphism algorithm to identify patterns of amino acid residues. Our methods are also applicable to other types of biological macromolecule, such as carbohydrate and nucleic acid structures