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Analytic Combinatorics for Computing Seeding Probabilities

Center for Genomic Regulation (CRG), The Barcelona Institute of Science and Technology, Dr. Aiguader 88, Barcelona 08003, Spain
University Pompeu Fabra, Dr. Aiguader 80, Barcelona 08003, Spain
Algorithms 2018, 11(1), 3;
Received: 12 November 2017 / Revised: 7 January 2018 / Accepted: 8 January 2018 / Published: 10 January 2018
(This article belongs to the Special Issue Bioinformatics Algorithms and Applications)
Seeding heuristics are the most widely used strategies to speed up sequence alignment in bioinformatics. Such strategies are most successful if they are calibrated, so that the speed-versus-accuracy trade-off can be properly tuned. In the widely used case of read mapping, it has been so far impossible to predict the success rate of competing seeding strategies for lack of a theoretical framework. Here, we present an approach to estimate such quantities based on the theory of analytic combinatorics. The strategy is to specify a combinatorial construction of reads where the seeding heuristic fails, translate this specification into a generating function using formal rules, and finally extract the probabilities of interest from the singularities of the generating function. The generating function can also be used to set up a simple recurrence to compute the probabilities with greater precision. We use this approach to construct simple estimators of the success rate of the seeding heuristic under different types of sequencing errors, and we show that the estimates are accurate in practical situations. More generally, this work shows novel strategies based on analytic combinatorics to compute probabilities of interest in bioinformatics. View Full-Text
Keywords: analytic combinatorics; bioinformatics; seeding sequence alignment; generating functions analytic combinatorics; bioinformatics; seeding sequence alignment; generating functions
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Filion, G.J. Analytic Combinatorics for Computing Seeding Probabilities. Algorithms 2018, 11, 3.

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