2 Search Results for "Cámara, Javier"

Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2020.3
List-Decodability of Structured Ensembles of Codes (Invited Talk)

Authors: Mary Wootters

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
What combinatorial properties are satisfied by a random subspace over a finite field? For example, is it likely that not too many points lie in any Hamming ball? What about any cube? In this talk, I will discuss the answer to these questions, along with a more general characterization of the properties that are likely to be satisfied by a random subspace. The motivation for this characterization comes from error correcting codes. I will discuss how to use this characterization to make progress on the questions of list-decoding and list-recovery for random linear codes, and also to establish the list-decodability of random Low Density Parity-Check (LDPC) codes. This talk is based on the works [Mosheiff et al., 2019] and [Guruswami et al., 2020], which are joint works with Venkatesan Guruswami, Ray Li, Jonathan Mosheiff, Nicolas Resch, Noga Ron-Zewi, and Shashwat Silas.
Cite as

Mary Wootters. List-Decodability of Structured Ensembles of Codes (Invited Talk). In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 3:1-3:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{wootters:LIPIcs.MFCS.2020.3,
  author =	{Wootters, Mary},
  title =	{{List-Decodability of Structured Ensembles of Codes}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{3:1--3:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.3},
  URN =		{urn:nbn:de:0030-drops-126742},
  doi =		{10.4230/LIPIcs.MFCS.2020.3},
  annote =	{Keywords: Error Correcting Codes, List-Decoding}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.20
List Homomorphism Problems for Signed Graphs

Authors: Jan Bok, Richard Brewster, Tomás Feder, Pavol Hell, and Nikola Jedličková

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
We consider homomorphisms of signed graphs from a computational perspective. In particular, we study the list homomorphism problem seeking a homomorphism of an input signed graph (G,σ), equipped with lists L(v) ⊆ V(H), v ∈ V(G), of allowed images, to a fixed target signed graph (H,π). The complexity of the similar homomorphism problem without lists (corresponding to all lists being L(v) = V(H)) has been previously classified by Brewster and Siggers, but the list version remains open and appears difficult. Both versions (with lists or without lists) can be formulated as constraint satisfaction problems, and hence enjoy the algebraic dichotomy classification recently verified by Bulatov and Zhuk. By contrast, we seek a combinatorial classification for the list version, akin to the combinatorial classification for the version without lists completed by Brewster and Siggers. We illustrate the possible complications by classifying the complexity of the list homomorphism problem when H is a (reflexive or irreflexive) signed tree. It turns out that the problems are polynomial-time solvable for certain caterpillar-like trees, and are NP-complete otherwise. The tools we develop will be useful for classifications of other classes of signed graphs, and we mention some follow-up research of this kind; those classifications are surprisingly complex.
Cite as

Jan Bok, Richard Brewster, Tomás Feder, Pavol Hell, and Nikola Jedličková. List Homomorphism Problems for Signed Graphs. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bok_et_al:LIPIcs.MFCS.2020.20,
  author =	{Bok, Jan and Brewster, Richard and Feder, Tom\'{a}s and Hell, Pavol and Jedli\v{c}kov\'{a}, Nikola},
  title =	{{List Homomorphism Problems for Signed Graphs}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.20},
  URN =		{urn:nbn:de:0030-drops-126886},
  doi =		{10.4230/LIPIcs.MFCS.2020.20},
  annote =	{Keywords: complexity, dichotomy, graph homomorphism, signed graph}
}
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