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On the readability of overlap digraphs

Rayan Chikhi 1, 2, 3, 4 Paul Medvedev 4 Martin Milanič 5 Sofya Raskhodnikova 4
1 BONSAI - Bioinformatics and Sequence Analysis
Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189, CNRS - Centre National de la Recherche Scientifique
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 behavior 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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Rayan Chikhi, Paul Medvedev, Martin Milanič, Sofya Raskhodnikova. On the readability of overlap digraphs. Discrete Applied Mathematics, Elsevier, 2016, 205, pp.35-44. ⟨10.1016/j.dam.2015.12.009⟩. ⟨hal-01729749⟩

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