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.
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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.
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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
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DOI: https://doi.org/10.1007/978-3-319-19929-0_11
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