Web Release Date: February 28,
Bounds and Algorithms for Fast Exact Searches of Chemical Fingerprints in Linear and Sublinear Time
Institute for Genomics and Bioinformatics, School of Information and Computer Sciences, University of California, Irvine, Irvine, California 92697-3435
Received August 16, 2006
Abstract:
Chemical fingerprints are used to represent chemical molecules by recording the presence or absence, or by
counting the number of occurrences, of particular features or substructures, such as labeled paths in the 2D
graph of bonds, of the corresponding molecule. These fingerprint vectors are used to search large databases
of small molecules, currently containing millions of entries, using various similarity measures, such as the
Tanimoto or Tversky's measures and their variants. Here, we derive simple bounds on these similarity
measures and show how these bounds can be used to considerably reduce the subset of molecules that need
to be searched. We consider both the case of single-molecule and multiple-molecule queries, as well as
queries based on fixed similarity thresholds or aimed at retrieving the top K hits. We study the speedup as
a function of query size and distribution, fingerprint length, similarity threshold, and database size 
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derive analytical formulas that are in excellent agreement with empirical values. The theoretical considerations
and experiments show that this approach can provide linear speedups of one or more orders of magnitude in
the case of searches with a fixed threshold, and achieve sublinear speedups in the range of O(D0.6) for
the top K hits in current large databases. This pruning approach yields subsecond search times across the 5
million compounds in the ChemDB database, without any loss of accuracy.
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