We introduce a new branch and bound algorithm for the maximum common subgraph and maximum common connected subgraph problems which is based around vertex labelling and partitioning. Our method in some ways resembles a traditional constraint programming approach, but uses a novel compact domain store and supporting inference algorithms which dramatically reduce the memory and computation require...

We discuss our experiences adapting three recent algorithms for maximum common (connected) subgraph problems to exploit multicore parallelism. These algorithms do not easily lend themselves to parallel search, as the search trees are extremely irregular, making balanced work distribution hard, and runtimes are very sensitive to value-ordering heuristic behaviour. Nonetheless, our results show t...

The maximum common subgraph problem is to find the largest subgraph common to two given graphs. This problem can be solved either by constraint-based search, or by reduction to the maximum clique problem. We evaluate these two models using modern algorithms, and see that the best choice depends mainly upon whether the graphs have labelled edges. We also study a variant of this problem where the...

Data fusion has been shown to work very well when applied to fingerprint-based similarity searching, yet little is known of its application to maximum common substructure (MCS)-based similarity searching. Two similarity search applications of the MCS will be focused on here. Typically, the number of bonds in the MCS, as well as the bonds in the two molecules being compared, are used in a simila...

We obtain new lower and upper bounds for the maximum multiplicity of some weighted, and respectively non-weighted, common geometric graphs drawn on n points in the plane in general position (with no three points collinear): perfect matchings, spanning trees, spanning cycles (tours), and triangulations. (i) We present a new lower bound construction for the maximum number of triangulations a set ...

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...

Radioiodinated rat CNS axolemmal fragments adhered to cultured rat Schwann cells by a time-, temperature-, and concentration-dependent process independent of extracellular ionized calcium. Adhesion showed target and signal specificity; axolemmal fragments adhered to endoneurial or dermal fibroblasts to a much lesser extent than to Schwann cells, and plasma membrane fragments from skeletal muscl...

Some versions of the maximum common subgraph problem are studied and approximation algorithms are given. The maximum bounded common induced subgraph problem is shown to be Max SNP-hard and the maximum unbounded common induced subgraph problem is shown to be as hard to approximate as the maximum independent set problem. The maximum common induced connected subgraph problem is still harder to app...

Despite dramatic improvements in the hardware resources and computational power available to pharmaceutical researchers over the past few decades, the methods used for assessing the 2D chemical similarity between two molecules hasn’t changed much since the 1960s. Here we report a novel chemical database search method that allows the exact size of the maximum common edge subgraph (MCES) between ...

Generalized maps are widely used to model the topology of nD objects (such as images) by means of incidence and adjacency relationships between cells (vertices, edges, faces, volumes, ...). In this paper, we introduce distance measures for comparing generalized maps, which is an important issue for image processing and analysis. We introduce a first distance measure which is defined by means of...