License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.08081.4
URN: urn:nbn:de:0030-drops-15291
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1529/
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Pettie, Seth
Sources of Superlinearity in Davenport-Schinzel Sequences
Abstract
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
@InProceedings{pettie:DagSemProc.08081.4,
author = {Pettie, Seth},
title = {{Sources of Superlinearity in Davenport-Schinzel Sequences}},
booktitle = {Data Structures},
pages = {1--14},
series = {Dagstuhl Seminar Proceedings (DagSemProc)},
ISSN = {1862-4405},
year = {2008},
volume = {8081},
editor = {Lars Arge and Robert Sedgewick and Raimund Seidel},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2008/1529},
URN = {urn:nbn:de:0030-drops-15291},
doi = {10.4230/DagSemProc.08081.4},
annote = {Keywords: Davenport-Schinzel Sequences, lower envelopes, splay trees}
}
Keywords: |
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Davenport-Schinzel Sequences, lower envelopes, splay trees |
Collection: |
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08081 - Data Structures |
Issue Date: |
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2008 |
Date of publication: |
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16.06.2008 |