Efficient Substructure Searching of Large Chemical Libraries: The ABCD Chemical Cartridge

Agrafiotis, Dimitris; Lobanov, Victor S.; Shemanarev, Maxim; Rassokhin, Dmitrii N.; Izrailev, Sergei; Jaeger, Edward P.; Alex, Simson; Farnum, Michael

doi:10.1021/ci200413e

Cited by 40 publications

(13 citation statements)

References 44 publications

(56 reference statements)

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“…Even though most database search systems are able to eliminate a large number of molecules from the actual subgraph isomorphism search using screening techniques [10,22,41,43-46], a remarkable number of molecules might remain. The following test simulates a sequential subgraph isomorphism test over a large set of molecules.…”

Section: Resultsmentioning

confidence: 99%

“…Furthermore, graphs allow the substructure search problem to be solved by graph isomorphism techniques, i.e., searching molecules for substructures is equivalent to testing two labeled graphs for subgraph isomorphism. The subgraph isomorphism problem is well studied [15-17] and one of the oldest and most applied algorithms [18-22] was introduced by Ullmann in 1976 [7]. Over the years that followed, only a few subgraph isomorphism methods were introduced [11,16,23], the most recent being the VF2 algorithm [12].…”

Section: Introductionmentioning

confidence: 99%

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

Ehrlich

Rarey

2012

J Cheminform

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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.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Ehrlich

Rarey

2012

J Cheminform

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“…Applications of pattern analysis using the subgraph isomorphism problem abound in various fields, such as chemistry [1,2], social network analysis [14], and computer vision [16] . Moreover, in these domains graph databases are replacing the traditional relational databases [3].…”

Section: Subgraph Isomorphism Problemmentioning

confidence: 99%

Search-Tree Size Estimation for the Subgraph Isomorphism Problem

Cibej¹,

Mihelič²

2018

AEI

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This article addresses the problem of finding patterns in graphs. This is formally defined as the subgraph isomorphism problem and is one of the core problems in theoretical computer science. We consider the counting variation of this problem. The task is to count all instances of the pattern G occurring in a (usually larger) graph H. The vast majority of algorithms for this problem use a variation of backtracking. Most commonly they exhaustively search through the space of all possible monomorphisms between G and H. The size of the search tree depends heavily on the choice of the ordering of vertices of G, which are systematically assigned to the vertices of H. We use a method called heuristic sampling to estimate the size of the search tree for each ordering in advance. We use this estimation to select the most suitable order of vertices of G which minimizes the expected tree size. This approach is empirically evaluated on a set of instances, showing the practical potential of the method.

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“…networks [1], all of which can be naturally modeled by graphs, graph representation and also algorithms on graphs are becoming increasingly important. Applications of graphs arise in various areas, ranging from chemistry [2], [3], economy [4], politics [5], to popular culture [6].…”

Section: Introductionmentioning

confidence: 99%

Maximum Exploratory Equivalence in Trees

Fürst

Cibej

Mihelič

2015

Annals of Computer Science and Information Systems

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Abstract-Many practical problems are modeled with networks and graphs. Their exploration is of significant importance, and several graph-exploration algorithms already exist. In this paper, we focus on a type of vertex equivalence, called exploratory equivalence, which has a great potential to speed up such algorithms. It is an equivalence based on graph automorphisms and can, for example, help us in solving the subgraph isomorphism problem, which is a well-known NP -hard problem. In particular, if a given pattern graph has nontrivial automorphisms, then each of its nontrivial exploratory equivalent classes gives rise to a set of constraints to prune the search space of solutions. In the paper, we define the maximum exploratory equivalence problem. We show that the defined problem is at least as hard the graph isomorphism problem. Additionally, we present a polynomial-time algorithm for solving the problem when the input is restricted to tree graphs. Furthermore, we show that for trees, a maximum exploratory equivalent partition leads to a globally optimal set of subgraph isomorphism constraints, whereas this is not necessarily the case for general graphs.

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Efficient Substructure Searching of Large Chemical Libraries: The ABCD Chemical Cartridge

Cited by 40 publications

References 44 publications

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

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

Search-Tree Size Estimation for the Subgraph Isomorphism Problem

Maximum Exploratory Equivalence in Trees

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