TY - JOUR

T1 - On the readability of overlap digraphs

AU - Chikhi, Rayan

AU - Medvedev, Paul

AU - Milanič, Martin

AU - Raskhodnikova, Sofya

N1 - Funding Information:
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(I0-0035, research program P1-0285 and research projects N1-0032, J1-5433, J1-6720, and J1-6743). S.R. was supported in part by NSF CAREER award CCF-0845701, NSF award AF-1422975, and Boston University's Hariri Institute for Computing and Center for Reliable Information Systems and Cyber Security.
Publisher Copyright:
© 2015 Elsevier B.V.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84952914729&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952914729&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2015.12.009

DO - 10.1016/j.dam.2015.12.009

M3 - Article

AN - SCOPUS:84952914729

SN - 0166-218X

VL - 205

SP - 35

EP - 44

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -