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Pettie, Seth

Sources of Superlinearity in Davenport-Schinzel Sequences

08081.PettieSeth.Paper.1529.pdf (0.5 MB)


A {em generalized} Davenport-Schinzel sequence is one over a finite alphabet that contains no subsequences isomorphic to a fixed {em forbidden subsequence}. One of the fundamental problems in this area is bounding (asymptotically) the maximum length of such sequences. Following Klazar, let $Ex(sigma,n)$ be the maximum length of a sequence over an alphabet of size $n$ avoiding subsequences isomorphic to $sigma$. It has been proved that for every $sigma$, $Ex(sigma,n)$ is either linear or very close to linear; in particular it is $O(n2^{alpha(n)^{O(1)}})$, where $alpha$ is the inverse-Ackermann function and $O(1)$ depends on $sigma$. However, very little is known about the properties of $sigma$ that induce superlinearity of $Ex(sigma,n)$. In this paper we exhibit an infinite family of independent superlinear forbidden subsequences. To be specific, we show that there are 17 {em prototypical} superlinear forbidden subsequences, some of which can be made arbitrarily long through a simple padding operation. Perhaps the most novel part of our constructions is a new succinct code for representing superlinear forbidden subsequences.

BibTeX - Entry

  author =	{Seth Pettie},
  title =	{Sources of Superlinearity in Davenport-Schinzel Sequences},
  booktitle =	{Data Structures},
  year =	{2008},
  editor =	{Lars Arge and Robert Sedgewick and Raimund Seidel},
  number =	{08081},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Davenport-Schinzel Sequences, lower envelopes, splay trees}

Keywords: Davenport-Schinzel Sequences, lower envelopes, splay trees
Seminar: 08081 - Data Structures
Issue Date: 2008
Date of publication: 16.06.2008

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