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Subwords in reverse-complement order

Authors: Péter L. Erdös, Péter Ligeti, Péter Sziklai, and David C. Torney

Published in: Dagstuhl Seminar Proceedings, Volume 6201, Combinatorial and Algorithmic Foundations of Pattern and Association Discovery (2006)

Abstract

We examine finite words over an alphabet $Gamma={a,bar{a};b,bar{b}}$ of pairs of letters, where each word $w_1w_2...w_t$ is identical with its {it reverse complement} $bar{w_t}...bar{w_2}bar{w_1}$ (where $bar{bbar{a}}=a,bar{bar{b}}=b$). We seek the smallest $k$ such that every word of length $n,$ composed from $Gamma$, is uniquely determined by the set of its subwords of length up to $k$. Our almost sharp result ($ksim 2n/3$) is an analogue of a classical result for ``normal'' words. This classical problem originally was posed by M.P. Sch"utzenberger and I. Simon, and gained a considerable interest for several researchers, foremost by Vladimir Levenshtein. Our problem has its roots in bioinformatics.

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Péter L. Erdös, Péter Ligeti, Péter Sziklai, and David C. Torney. Subwords in reverse-complement order. In Combinatorial and Algorithmic Foundations of Pattern and Association Discovery. Dagstuhl Seminar Proceedings, Volume 6201, pp. 1-8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{erdos_et_al:DagSemProc.06201.10,
  author =	{Erd\"{o}s, P\'{e}ter L. and Ligeti, P\'{e}ter and Sziklai, P\'{e}ter and Torney, David C.},
  title =	{{Subwords in reverse-complement order}},
  booktitle =	{Combinatorial and Algorithmic Foundations of Pattern and Association Discovery},
  pages =	{1--8},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6201},
  editor =	{Rudolf Ahlswede and Alberto Apostolico and Vladimir I. Levenshtein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06201.10},
  URN =		{urn:nbn:de:0030-drops-7856},
  doi =		{10.4230/DagSemProc.06201.10},
  annote =	{Keywords: Reverse complement order, Reconstruction of words, Microarray experiments}
}

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Subwords in reverse-complement order

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