Abstract
The Shortest Superstring Problem (SSP) consists, for a set of strings \(S = \{s_1,\cdots ,s_n\}\) (with no \(s_i\) substring of \(s_j\)), to find a minimum length string that contains all \(s_i, 1\le i \le n\), as substrings.
This problem is proved to be NP-Complete and APX-hard. Guaranteed approximation algorithms have been proposed, the current best ratio being \(2\frac{11}{30}\), which has been achieved through a long and difficult process. SSP is highly used in practice on Next Generation Sequencing (NGS) data, which plays an increasingly important role in modern biological and medical research. In this note, we show that on NGS data the SSP approximation ratio reached by the classical algorithm of Blum et al. [2], is usually below \(2\frac{11}{30}\), while assuming specific characteristics of the data that are experimentally verified on a large sampling set. Moreover, we present an efficient linear time test for any input of strings of equal length, which allows to compute the approximation ratio that can be reached using the classical algorithm in [2].
This work was supported by the PEPS INS2I-CNRS project CompX and by a Genotype to Phenotype project of the Life Sciences Department of University of Bordeaux.
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Braquelaire, T., Gasparoux, M., Raffinot, M., Uricaru, R. (2017). On the Shortest Common Superstring of NGS Reads. In: Gopal, T., Jäger , G., Steila, S. (eds) Theory and Applications of Models of Computation. TAMC 2017. Lecture Notes in Computer Science(), vol 10185. Springer, Cham. https://doi.org/10.1007/978-3-319-55911-7_8
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