Systematic benchmark of substructure search in molecular graphs - From Ullmann to VF2

Abstract

BackgroundSearching for substructures in molecules belongs to the most elementary tasks in cheminformatics and is nowadays part of virtually every cheminformatics software. The underlying algorithms, used over several decades, are designed for the application to general graphs. Applied on molecular graphs, little effort has been spend on characterizing their performance. Therefore, it is not clear how current substructure search algorithms behave on such special graphs. One of the main reasons why such an evaluation was not performed in the past was the absence of appropriate data sets.ResultsIn this paper, we present a systematic evaluation of Ullmann’s and the VF2 subgraph isomorphism algorithms on molecular data. The benchmark set consists of a collection of 1235 SMARTS substructure expressions and selected molecules from the ZINC database. The benchmark evaluates substructures search times for complete database scans as well as individual substructure-molecule pairs. In detail, we focus on the influence of substructure formulation and size, the impact of molecule size, and the ability of both algorithms to be used on multiple cores.ConclusionsThe results show a clear superiority of the VF2 algorithm in all test scenarios. In general, both algorithms solve most instances in less than one millisecond, which we consider to be acceptable. Still, in direct comparison, the VF2 is most often several folds faster than Ullmann’s algorithm. Additionally, Ullmann’s algorithm shows a surprising number of run time outliers.

Technical Note: Development of chemoinformatic tools to enumerate functional groups in molecules for organic aerosol characterization

“…The concept of using SMILES and SMARTS patterns has been reported for applications in the atmospheric chemistry community (Barley et al, 2011;COBRA, Fooshee et al, 2012). While some sets of SMARTS patterns for substructure matching can additionally be found in the literature (Hann et al, 1999;Walters and Murcko, 2002;Olah et al, 2004;Enoch et al, 2008;Barley et al, 2011;Kenny et al, 2013) or on web databases -e.g., DAYLIGHT Chemical Information Systems, Inc. (DAYLIGHT Chemical Information Systems, Inc.) -knowledge regarding the extent of specificity and validation of the defined patterns is not available.…”

“…For this task, the aerosol community can benefit from developments in the chemoinformatics community. If the structure of a substance is described through its molecular (also referred to as chemical) graph (Balaban, 1985) -which is a set of atoms and their association through bonds -the abundance of arbitrary substructures (also called fragments) can be estimated through pattern-matching algorithms called subgraph isomorphisms (Barnard, 1993;Ehrlich and Rarey, 2012;Kerber et al, 2014). Structural information of molecules can be encoded in various representations, including a linear string of ASCII characters denoted as SMILES (Weininger, 1988).…”

CONFECT: Conformations from an Expert Collection of Torsion Patterns

“…[22] Due to the pattern hierarchy, this assignment is unique. Each torsion pattern is associated with a list of preferred torsion angles, its relative frequency, and tolerances as described previously.…”

Learning Kinematic Structure Correspondences Using Multi-Order Similarities

“…4 represents an example of a subgraph isomorphism of G to G . To find the subgraph isomorphisms, we use the VF2 algorithm [65] 1 , which is one of the most recent methods and has shown a clear superiority in different scenarios [66]. The output of VF2 is a set of binary assignment matrices X = {X 1 , · · · , X L }, with each assignment matrix…”