On the readability of overlap digraphs

Rayan Chikhi, Paul Medvedev, Martin Milanič, Sofya Raskhodnikova

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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.

Original languageEnglish (US)
Pages (from-to)35-44
Number of pages10
JournalDiscrete Applied Mathematics
Volume205
DOIs
StatePublished - Jan 1 2016

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All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Chikhi, R., Medvedev, P., Milanič, M., & Raskhodnikova, S. (2016). On the readability of overlap digraphs. Discrete Applied Mathematics, 205, 35-44. https://doi.org/10.1016/j.dam.2015.12.009