2 Search Results for "Severini, Lorenzo"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.37
Satisfiability of Commutative vs. Non-Commutative CSPs

Authors: Andrei A. Bulatov and Stanislav Živný

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
The Mermin-Peres magic square is a celebrated example of a system of Boolean linear equations that is not (classically) satisfiable but is satisfiable via linear operators on a Hilbert space of dimension four. A natural question is then, for what kind of problems such a phenomenon occurs? Atserias, Kolaitis, and Severini answered this question for all Boolean Constraint Satisfaction Problems (CSPs): For 0-Valid-SAT, 1-Valid-SAT, 2-SAT, Horn-SAT, and Dual Horn-SAT, classical satisfiability and operator satisfiability is the same and thus there is no gap; for all other Boolean CSPs, these notions differ as there are gaps, i.e., there are unsatisfiable instances that are satisfiable via operators on Hilbert spaces. We generalize their result to CSPs on arbitrary finite domains and give an almost complete classification: First, we show that NP-hard CSPs admit a separation between classical satisfiability and satisfiability via operators on finite- and infinite-dimensional Hilbert spaces. Second, we show that tractable CSPs of bounded width have no satisfiability gaps of any kind. Finally, we show that tractable CSPs of unbounded width can simulate, in a satisfiability-gap-preserving fashion, linear equations over an Abelian group of prime order p; for such CSPs, we obtain a separation of classical satisfiability and satisfiability via operators on infinite-dimensional Hilbert spaces. Furthermore, if p = 2, such CSPs also have gaps separating classical satisfiability and satisfiability via operators on finite- and infinite-dimensional Hilbert spaces.
Cite as

Andrei A. Bulatov and Stanislav Živný. Satisfiability of Commutative vs. Non-Commutative CSPs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bulatov_et_al:LIPIcs.ICALP.2025.37,
  author =	{Bulatov, Andrei A. and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Satisfiability of Commutative vs. Non-Commutative CSPs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{37:1--37:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.37},
  URN =		{urn:nbn:de:0030-drops-234149},
  doi =		{10.4230/LIPIcs.ICALP.2025.37},
  annote =	{Keywords: constraint satisfaction, quantum CSP, operator CSP}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.75
Selecting Nodes and Buying Links to Maximize the Information Diffusion in a Network

Authors: Gianlorenzo D'Angelo, Lorenzo Severini, and Yllka Velaj

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
The Independent Cascade Model (ICM) is a widely studied model that aims to capture the dynamics of the information diffusion in social networks and in general complex networks. In this model, we can distinguish between active nodes which spread the information and inactive ones. The process starts from a set of initially active nodes called seeds. Recursively, currently active nodes can activate their neighbours according to a probability distribution on the set of edges. After a certain number of these recursive cycles, a large number of nodes might become active. The process terminates when no further node gets activated. Starting from the work of Domingos and Richardson [Domingos et al. 2001], several studies have been conducted with the aim of shaping a given diffusion process so as to maximize the number of activated nodes at the end of the process. One of the most studied problems has been formalized by Kempe et al. and consists in finding a set of initial seeds that maximizes the expected number of active nodes under a budget constraint [Kempe et al. 2003]. In this paper we study a generalization of the problem of Kempe et al. in which we are allowed to spend part of the budget to create new edges incident to the seeds. That is, the budget can be spent to buy seeds or edges according to a cost function. The problem does not admin a PTAS, unless P=NP. We propose two approximation algorithms: the former one gives an approximation ratio that depends on the edge costs and increases when these costs are high; the latter algorithm gives a constant approximation guarantee which is greater than that of the first algorithm when the edge costs can be small.
Cite as

Gianlorenzo D'Angelo, Lorenzo Severini, and Yllka Velaj. Selecting Nodes and Buying Links to Maximize the Information Diffusion in a Network. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 75:1-75:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{dangelo_et_al:LIPIcs.MFCS.2017.75,
  author =	{D'Angelo, Gianlorenzo and Severini, Lorenzo and Velaj, Yllka},
  title =	{{Selecting Nodes and Buying Links to Maximize the Information Diffusion in a Network}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{75:1--75:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.75},
  URN =		{urn:nbn:de:0030-drops-80853},
  doi =		{10.4230/LIPIcs.MFCS.2017.75},
  annote =	{Keywords: Approximation algorithms, information diffusion, complex networks, independent cascade model, network augmentation}
}
  • Refine by Type
  • 2 Document/PDF
  • 1 Document/HTML

  • Refine by Publication Year
  • 1 2025
  • 1 2017

  • Refine by Author
  • 1 Bulatov, Andrei A.
  • 1 D'Angelo, Gianlorenzo
  • 1 Severini, Lorenzo
  • 1 Velaj, Yllka
  • 1 Živný, Stanislav

  • Refine by Series/Journal
  • 2 LIPIcs

  • Refine by Classification
  • 1 Theory of computation → Design and analysis of algorithms
  • 1 Theory of computation → Problems, reductions and completeness

  • Refine by Keyword
  • 1 Approximation algorithms
  • 1 complex networks
  • 1 constraint satisfaction
  • 1 independent cascade model
  • 1 information diffusion
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact