3 Search Results for "Defant, Colin"

Document
DOI: 10.4230/LIPIcs.CPM.2026.14
Hardness Results on Characteristics for Elastic-Degenerate Strings

Authors: Dominik Köppl and Jannik Olbrich

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
Generalizations of plain strings have been proposed as a compact way to represent a collection of nearly identical sequences or to express uncertainty at specific text positions by enumerating all possibilities. While a plain string stores a character at each of its positions, generalizations consider a set of characters (indeterminate strings), a set of strings of equal length (generalized degenerate strings, or shortly GD strings), or a set of strings of arbitrary lengths (elastic-degenerate strings, or shortly ED strings). These generalizations are of importance to compactly represent such type of data, and find applications in bioinformatics for representing and maintaining a set of genetic sequences of the same taxonomy or a multiple sequence alignment. To be of use, attention has been drawn to answering various query types such as pattern matching or measuring similarity of ED strings by generalizing techniques known to plain strings. However, for some types of queries, it has been shown that a generalization of a polynomial-time solvable query on classic strings becomes NP-hard on ED strings, e.g. [Russo et al., 2022]. In that light, we wonder about other types of queries that are of particular interest to bioinformatics: unique substrings, absent words, anti-powers, longest previous factors, and Lempel-Ziv-like compression schemes. While we obtain a polynomial time algorithm for a variation of longest previous factors, we show that all other problems are NP-hard to compute, some of them even under the restriction that the input can be modeled as an indeterminate or GD string.
Cite as

Dominik Köppl and Jannik Olbrich. Hardness Results on Characteristics for Elastic-Degenerate Strings. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 14:1-14:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{koppl_et_al:LIPIcs.CPM.2026.14,
  author =	{K\"{o}ppl, Dominik and Olbrich, Jannik},
  title =	{{Hardness Results on Characteristics for Elastic-Degenerate Strings}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{14:1--14:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.14},
  URN =		{urn:nbn:de:0030-drops-259409},
  doi =		{10.4230/LIPIcs.CPM.2026.14},
  annote =	{Keywords: Elastic-degenerate strings, NP-hardness, longest common factor, minimal unique substring, minimal absent word, anti-power, longest previous factor}
}
Document
DOI: 10.4230/OASIcs.AUTOMATA.2021.5
Dynamical Algebraic Combinatorics, Asynchronous Cellular Automata, and Toggling Independent Sets

Authors: Laurent David, Colin Defant, Michael Joseph, Matthew Macauley, and Alex McDonough

Published in: OASIcs, Volume 90, 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)

Abstract
Though iterated maps and dynamical systems are not new to combinatorics, they have enjoyed a renewed prominence over the past decade through the elevation of the subfield that has become known as dynamical algebraic combinatorics. Some of the problems that have gained popularity can also be cast and analyzed as finite asynchronous cellular automata (CA). However, these two fields are fairly separate, and while there are some individuals who work in both, that is the exception rather than the norm. In this article, we will describe our ongoing work on toggling independent sets on graphs. This will be preceded by an overview of how this project arose from new combinatorial problems involving homomesy, toggling, and resonance. Though the techniques that we explore are directly applicable to ECA rule 1, many of them can be generalized to other cellular automata. Moreover, some of the ideas that we borrow from cellular automata can be adapted to problems in dynamical algebraic combinatorics. It is our hope that this article will inspire new problems in both fields and connections between them.
Cite as

Laurent David, Colin Defant, Michael Joseph, Matthew Macauley, and Alex McDonough. Dynamical Algebraic Combinatorics, Asynchronous Cellular Automata, and Toggling Independent Sets. In 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021). Open Access Series in Informatics (OASIcs), Volume 90, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{david_et_al:OASIcs.AUTOMATA.2021.5,
  author =	{David, Laurent and Defant, Colin and Joseph, Michael and Macauley, Matthew and McDonough, Alex},
  title =	{{Dynamical Algebraic Combinatorics, Asynchronous Cellular Automata, and Toggling Independent Sets}},
  booktitle =	{27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)},
  pages =	{5:1--5:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-189-4},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{90},
  editor =	{Castillo-Ramirez, Alonso and Guillon, Pierre and Perrot, K\'{e}vin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.AUTOMATA.2021.5},
  URN =		{urn:nbn:de:0030-drops-140145},
  doi =		{10.4230/OASIcs.AUTOMATA.2021.5},
  annote =	{Keywords: Asynchronous cellular automata, Covering space, Coxeter element, Dynamical algebraic combinatorics, Group action, Homomesy, Independent set, Resonance, Toggling, Toric equivalence}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.18
Circular Trace Reconstruction

Authors: Shyam Narayanan and Michael Ren

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
Trace reconstruction is the problem of learning an unknown string x from independent traces of x, where traces are generated by independently deleting each bit of x with some deletion probability q. In this paper, we initiate the study of Circular trace reconstruction, where the unknown string x is circular and traces are now rotated by a random cyclic shift. Trace reconstruction is related to many computational biology problems studying DNA, which is a primary motivation for this problem as well, as many types of DNA are known to be circular. Our main results are as follows. First, we prove that we can reconstruct arbitrary circular strings of length n using exp(Õ(n^{1/3})) traces for any constant deletion probability q, as long as n is prime or the product of two primes. For n of this form, this nearly matches what was the best known bound of exp(O(n^{1/3})) for standard trace reconstruction when this paper was initially released. We note, however, that Chase very recently improved the standard trace reconstruction bound to exp(Õ(n^{1/5})). Next, we prove that we can reconstruct random circular strings with high probability using n^O(1) traces for any constant deletion probability q. Finally, we prove a lower bound of Ω̃(n³) traces for arbitrary circular strings, which is greater than the best known lower bound of Ω̃(n^{3/2}) in standard trace reconstruction.
Cite as

Shyam Narayanan and Michael Ren. Circular Trace Reconstruction. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{narayanan_et_al:LIPIcs.ITCS.2021.18,
  author =	{Narayanan, Shyam and Ren, Michael},
  title =	{{Circular Trace Reconstruction}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.18},
  URN =		{urn:nbn:de:0030-drops-135573},
  doi =		{10.4230/LIPIcs.ITCS.2021.18},
  annote =	{Keywords: Trace Reconstruction, Deletion Channel, Cyclotomic Integers}
}
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