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Parameterized Approximation: Algorithms and Hardness (Dagstuhl Seminar 23291)

Authors: Karthik C. S., Parinya Chalermsook, Joachim Spoerhase, Meirav Zehavi, and Martin Herold

Published in: Dagstuhl Reports, Volume 13, Issue 7 (2024)

Abstract

Parameterization and approximation are two established approaches of coping with intractability in combinatorial optimization. In this Dagstuhl Seminar, we studied parameterized approximation as a relatively new algorithmic paradigm that combines these two popular research areas. In particular, we analyzed the solution quality (approximation ratio) as well as the running time of an algorithm in terms of a parameter that captures the "complexity" of a problem instance. While the field has grown and yielded some promising results, our understanding of the area is rather ad-hoc compared to our knowledge in approximation or parameterized algorithms alone. In this seminar, we brought together researchers from both communities in order to bridge this gap by accommodating the exchange and unification of scientific knowledge.

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Karthik C. S., Parinya Chalermsook, Joachim Spoerhase, Meirav Zehavi, and Martin Herold. Parameterized Approximation: Algorithms and Hardness (Dagstuhl Seminar 23291). In Dagstuhl Reports, Volume 13, Issue 7, pp. 96-107, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{c.s._et_al:DagRep.13.7.96,
  author =	{C. S., Karthik and Chalermsook, Parinya and Spoerhase, Joachim and Zehavi, Meirav and Herold, Martin},
  title =	{{Parameterized Approximation: Algorithms and Hardness (Dagstuhl Seminar 23291)}},
  pages =	{96--107},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{7},
  editor =	{C. S., Karthik and Chalermsook, Parinya and Spoerhase, Joachim and Zehavi, Meirav and Herold, Martin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.7.96},
  URN =		{urn:nbn:de:0030-drops-197764},
  doi =		{10.4230/DagRep.13.7.96},
  annote =	{Keywords: approximation algorithms, Hardness of approximation, Parameterized algorithms}
}

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DOI: 10.4230/LIPIcs.MFCS.2023.44

Upward Translation of Optimal and P-Optimal Proof Systems in the Boolean Hierarchy over NP

Authors: Fabian Egidy, Christian Glaßer, and Martin Herold

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract

We study the existence of optimal and p-optimal proof systems for classes in the Boolean hierarchy over NP. Our main results concern DP, i.e., the second level of this hierarchy: - If all sets in DP have p-optimal proof systems, then all sets in coDP have p-optimal proof systems. - The analogous implication for optimal proof systems fails relative to an oracle. As a consequence, we clarify such implications for all classes 𝒞 and 𝒟 in the Boolean hierarchy over NP: either we can prove the implication or show that it fails relative to an oracle. Furthermore, we show that the sets SAT and TAUT have p-optimal proof systems, if and only if all sets in the Boolean hierarchy over NP have p-optimal proof systems which is a new characterization of a conjecture studied by Pudlák.

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Fabian Egidy, Christian Glaßer, and Martin Herold. Upward Translation of Optimal and P-Optimal Proof Systems in the Boolean Hierarchy over NP. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 44:1-44:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{egidy_et_al:LIPIcs.MFCS.2023.44,
  author =	{Egidy, Fabian and Gla{\ss}er, Christian and Herold, Martin},
  title =	{{Upward Translation of Optimal and P-Optimal Proof Systems in the Boolean Hierarchy over NP}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{44:1--44:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.44},
  URN =		{urn:nbn:de:0030-drops-185784},
  doi =		{10.4230/LIPIcs.MFCS.2023.44},
  annote =	{Keywords: Computational Complexity, Boolean Hierarchy, Proof Complexity, Proof Systems, Oracle Construction}
}

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Parameterized Approximation: Algorithms and Hardness (Dagstuhl Seminar 23291)

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Upward Translation of Optimal and P-Optimal Proof Systems in the Boolean Hierarchy over NP

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