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Documents authored by Pape-Lange, Julian


Document
On Extensions of Maximal Repeats in Compressed Strings

Authors: Julian Pape-Lange

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)


Abstract
This paper provides upper bounds for several subsets of maximal repeats and maximal pairs in compressed strings and also presents a formerly unknown relationship between maximal pairs and the run-length Burrows-Wheeler transform. This relationship is used to obtain a different proof for the Burrows-Wheeler conjecture which has recently been proven by Kempa and Kociumaka in "Resolution of the Burrows-Wheeler Transform Conjecture". More formally, this paper proves that the run-length Burrows-Wheeler transform of a string S with z_S LZ77-factors has at most 73(log₂ |S|)(z_S+2)² runs, and if S does not contain q-th powers, the number of arcs in the compacted directed acyclic word graph of S is bounded from above by 18q(1+log_q |S|)(z_S+2)².

Cite as

Julian Pape-Lange. On Extensions of Maximal Repeats in Compressed Strings. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 27:1-27:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{papelange:LIPIcs.CPM.2020.27,
  author =	{Pape-Lange, Julian},
  title =	{{On Extensions of Maximal Repeats in Compressed Strings}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{27:1--27:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.27},
  URN =		{urn:nbn:de:0030-drops-121523},
  doi =		{10.4230/LIPIcs.CPM.2020.27},
  annote =	{Keywords: Maximal repeats, Extensions of maximal repeats, Combinatorics on compressed strings, LZ77, Burrows-Wheeler transform, Burrows-Wheeler transform conjecture, Compact suffix automata, CDAWGs}
}
Document
Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements

Authors: Mitsuru Funakoshi and Julian Pape-Lange

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
The discrete acyclic convolution computes the 2n+1 sums ∑_{i+j=k|(i,j)∈[0,1,2,… ,n]²} a_i b_j in ?(n log n) time. By using suitable offsets and setting some of the variables to zero, this method provides a tool to calculate all non-zero sums ∑_{i+j=k|(i,j)∈ P∩ℤ²} a_i b_j in a rectangle P with perimeter p in ?(p log p) time. This paper extends this geometric interpretation in order to allow arbitrary convex polygons P with k vertices and perimeter p. Also, this extended algorithm only needs ?(k + p(log p)² log k) time. Additionally, this paper presents fast algorithms for counting sub-cadences and cadences with 3 elements using this extended method.

Cite as

Mitsuru Funakoshi and Julian Pape-Lange. Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 30:1-30:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{funakoshi_et_al:LIPIcs.STACS.2020.30,
  author =	{Funakoshi, Mitsuru and Pape-Lange, Julian},
  title =	{{Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.30},
  URN =		{urn:nbn:de:0030-drops-118911},
  doi =		{10.4230/LIPIcs.STACS.2020.30},
  annote =	{Keywords: discrete acyclic convolutions, string-cadences, geometric algorithms, number theoretic transforms}
}
Document
On Maximal Repeats in Compressed Strings

Authors: Julian Pape-Lange

Published in: LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)


Abstract
This paper presents and proves a new non-trivial upper bound on the number of maximal repeats of compressed strings. Using Theorem 1 of Raffinot’s article "On Maximal Repeats in Strings", this upper bound can be directly translated into an upper bound on the number of nodes in the Compacted Directed Acyclic Word Graphs of compressed strings. More formally, this paper proves that the number of maximal repeats in a string with z (self-referential) LZ77-factors and without q-th powers is at most 3q(z+1)^3-2. Also, this paper proves that for 2000 <= z <= q this upper bound is tight up to a constant factor.

Cite as

Julian Pape-Lange. On Maximal Repeats in Compressed Strings. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 18:1-18:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@InProceedings{papelange:LIPIcs.CPM.2019.18,
  author =	{Pape-Lange, Julian},
  title =	{{On Maximal Repeats in Compressed Strings}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-103-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{128},
  editor =	{Pisanti, Nadia and P. Pissis, Solon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.18},
  URN =		{urn:nbn:de:0030-drops-104898},
  doi =		{10.4230/LIPIcs.CPM.2019.18},
  annote =	{Keywords: Maximal repeats, Combinatorics on compressed strings, LZ77, Compact suffix automata, CDAWGs}
}
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