Abstract
We introduce the graph parameter readability and study it as a function of the number of vertices in a graph. Given a digraph \(D\), an injective overlap labeling assigns a unique string to each vertex such that there is an arc from \(x\) to \(y\) if and only if \(x\) properly overlaps \(y\). The readability of \(D\) is the minimum string length for which an injective overlap labeling exists. In applications that utilize overlap digraphs (e.g., in bioinformatics), readability reflects the length of the strings from which the overlap digraph is constructed. We study the asymptotic behaviour of readability by casting it in purely graph theoretic terms (without any reference to strings). We prove upper and lower bounds on readability for certain graph families and general graphs.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bresler, G., Bresler, M., Tse, D.: Optimal assembly for high throughput shotgun sequencing. BMC Bioinform. 14(Suppl 5), S18 (2013)
Błażewicz, J., Formanowicz, P., Kasprzak, M., Schuurman, P., Woeginger, G.J.: DNA sequencing, eulerian graphs, and the exact perfect matching problem. In: Kučera, L. (ed.) WG 2002. LNCS, vol. 2573, pp. 13–24. Springer, Heidelberg (2002)
Błażewicz, J., Formanowicz, P., Kasprzak, M., Kobler, D.: On the recognition of de Bruijn graphs and their induced subgraphs. Discrete Math. 245(1), 81–92 (2002)
Blazewicz, J., Hertz, A., Kobler, D., de Werra, D.: On some properties of DNA graphs. Discrete Appl. Math. 98(1), 1–19 (1999)
Braga, M.D.V., Meidanis, J.: An algorithm that builds a set of strings given its overlap graph. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, p. 52. Springer, Heidelberg (2002)
Bondy, J.A., Murty, U.S.R.: Graph Theory. Graduate Texts in Mathematics., vol. 244. Springer, New York (2008)
Gevezes, T.P., Pitsoulis, L.S.: Recognition of overlap graphs. J. Comb. Optim. 28(1), 25–37 (2014)
Idury, R.M., Waterman, M.S.: A new algorithm for DNA sequence assembly. J. Comput. Biol. 2(2), 291–306 (1995)
Li, X., Zhang, H.: Characterizations for some types of DNA graphs. J. Math. Chem. 42(1), 65–79 (2007)
Li, X., Zhang, H.: Embedding on alphabet overlap digraphs. J. Math. Chem. 47(1), 62–71 (2010)
Medvedev, P., Georgiou, K., Myers, G., Brudno, M.: Computability of models for sequence assembly. In: Giancarlo, R., Hannenhalli, S. (eds.) WABI 2007. LNCS (LNBI), vol. 4645, pp. 289–301. Springer, Heidelberg (2007)
Miller, J.R., Koren, S., Sutton, G.: Assembly algorithms for next-generation sequencing data. Genomics 95(6), 315–327 (2010)
Myers, E.W.: The fragment assembly string graph. In: ECCB/JBI, pp. 85 (2005)
Nagarajan, N., Pop, M.: Parametric complexity of sequence assembly: theory and applications to next generation sequencing. J. Comput. Biol. 16(7), 897–908 (2009)
Nagarajan, N., Pop, M.: Sequence assembly demystified. Nat. Rev. Genet. 14(3), 157–167 (2013)
Pendavingh, R., Schuurman, P., Woeginger, G.J.: Recognizing DNA graphs is difficult. Discrete Appl. Math. 127(1), 85–94 (2003)
Sweedyk, Z.: A 2\(\frac{1}{2}\)-approximation algorithm for shortest superstring. SIAM J. Comput. 29(3), 954–986 (2000)
Tarhio, J., Ukkonen, E.: A greedy approximation algorithm for constructing shortest common superstrings. Theor. Comput. Sci. 57(1), 131–145 (1988)
Acknowledgements
P.M. and M.M. would like to thank Marcin Kamiński for preliminary discussions. P.M. was supported in part by NSF awards DBI-1356529 and CAREER award IIS-1453527. M.M. was supported in part by the Slovenian Research Agency (I\(0\)-\(0035\), research program P\(1\)-\(0285\) and research projects N\(1\)-\(0032\), J\(1\)-\(5433\), J\(1\)-\(6720\), and J\(1\)-\(6743\)). S.R. was supported in part by NSF CAREER award CCF-0845701, NSF award AF-1422975 and the Hariri Institute for Computing and Computational Science and Engineering at Boston University.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Chikhi, R., Medvedev, P., Milanič, M., Raskhodnikova, S. (2015). On the Readability of Overlap Digraphs. In: Cicalese, F., Porat, E., Vaccaro, U. (eds) Combinatorial Pattern Matching. CPM 2015. Lecture Notes in Computer Science(), vol 9133. Springer, Cham. https://doi.org/10.1007/978-3-319-19929-0_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-19929-0_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19928-3
Online ISBN: 978-3-319-19929-0
eBook Packages: Computer ScienceComputer Science (R0)