Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Apostolico, Alberto; Pizzi, Cinzia License
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URN: urn:nbn:de:0030-drops-7899
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On the Monotonicity of the String Correction Factor for Words with Mismatches

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Abstract

The string correction factor is the term by
which the probability of a word $w$ needs to be multiplied in order
to account for character changes or ``errors'' occurring in at most
$k$ arbitrary positions in that word. The behavior of this factor,
as a function of $k$ and of the word length, has implications on the
number of candidates that need to be considered and weighted when
looking for subwords of a sequence that present unusually recurrent
replicas within some bounded number of mismatches. Specifically, it
is seen that over intervals of mono- or bi-tonicity for the
correction factor, only some of the candidates need be considered.
This mitigates the computation and leads to tables of
over-represented words that are more compact to represent and
inspect. In recent work, expectation and score monotonicity has been
established for a number of cases of interest, under {em i.i.d.}
probabilistic assumptions. The present paper reviews the cases of
bi-tonic behavior for the correction factor, concentrating on the
instance in which the question is still open.


BibTeX - Entry

@InProceedings{apostolico_et_al:DagSemProc.06201.5,
  author =	{Apostolico, Alberto and Pizzi, Cinzia},
  title =	{{On the Monotonicity of the String Correction Factor for Words with Mismatches}},
  booktitle =	{Combinatorial and Algorithmic Foundations of Pattern and Association Discovery},
  pages =	{1--9},
  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/opus/volltexte/2006/789},
  URN =		{urn:nbn:de:0030-drops-7899},
  doi =		{10.4230/DagSemProc.06201.5},
  annote =	{Keywords: Pattern discovery, Motif, Over-represented word, Monotone score, Correction Factor}
}

Keywords: Pattern discovery, Motif, Over-represented word, Monotone score, Correction Factor
Seminar: 06201 - Combinatorial and Algorithmic Foundations of Pattern and Association Discovery
Issue date: 2006
Date of publication: 07.11.2006


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