4 Search Results for "Hetterich, Samuel"

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.48
Sharp Thresholds for the Overlap Gap Property: Ising p-Spin Glass and Random k-SAT

Authors: Eren C. Kızıldağ

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
The Ising p-spin glass and random k-SAT are two canonical examples of disordered systems that play a central role in understanding the link between geometric features of optimization landscapes and computational tractability. Both models exhibit hard regimes where all known polynomial-time algorithms fail and possess the multi Overlap Gap Property (m-OGP), an intricate geometrical property that rigorously rules out a broad class of algorithms exhibiting input stability. We establish that, in both models, the symmetric m-OGP undergoes a sharp phase transition, and we pinpoint its exact threshold. For the Ising p-spin glass, our results hold for all sufficiently large p; for the random k-SAT, they apply to all k growing mildly with the number of Boolean variables. Notably, our findings yield qualitative insights into the power of OGP-based arguments. A particular consequence for the Ising p-spin glass is that the strength of the m-OGP in establishing algorithmic hardness grows without bound as m increases. These are the first sharp threshold results for the m-OGP. Our analysis hinges on a judicious application of the second moment method, enhanced by concentration. While a direct second moment calculation fails, we overcome this via a refined approach that leverages an argument of Frieze [Frieze, 1990] and exploiting concentration properties of carefully constructed random variables.
Cite as

Eren C. Kızıldağ. Sharp Thresholds for the Overlap Gap Property: Ising p-Spin Glass and Random k-SAT. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kizildag:LIPIcs.APPROX/RANDOM.2025.48,
  author =	{K{\i}z{\i}lda\u{g}, Eren C.},
  title =	{{Sharp Thresholds for the Overlap Gap Property: Ising p-Spin Glass and Random k-SAT}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{48:1--48:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.48},
  URN =		{urn:nbn:de:0030-drops-244147},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.48},
  annote =	{Keywords: spin glasses, p-spin model, random constraint satisfaction problems, overlap gap property, phase transitions, computational complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.47
Belief Propagation Guided Decimation on Random k-XORSAT

Authors: Arnab Chatterjee, Amin Coja-Oghlan, Mihyun Kang, Lena Krieg, Maurice Rolvien, and Gregory B. Sorkin

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

Abstract
We analyse the performance of Belief Propagation Guided Decimation, a physics-inspired message passing algorithm, on the random k-XORSAT problem. Specifically, we derive an explicit threshold up to which the algorithm succeeds with a strictly positive probability Ω(1) that we compute explicitly, but beyond which the algorithm with high probability fails to find a satisfying assignment. In addition, we analyse a thought experiment called the decimation process for which we identify a (non-) reconstruction and a condensation phase transition. The main results of the present work confirm physics predictions from [Ricci-Tersenghi and Semerjian: J. Stat. Mech. 2009] that link the phase transitions of the decimation process with the performance of the algorithm, and improve over partial results from a recent article [Yung: Proc. ICALP 2024].
Cite as

Arnab Chatterjee, Amin Coja-Oghlan, Mihyun Kang, Lena Krieg, Maurice Rolvien, and Gregory B. Sorkin. Belief Propagation Guided Decimation on Random k-XORSAT. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 47:1-47:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chatterjee_et_al:LIPIcs.ICALP.2025.47,
  author =	{Chatterjee, Arnab and Coja-Oghlan, Amin and Kang, Mihyun and Krieg, Lena and Rolvien, Maurice and Sorkin, Gregory B.},
  title =	{{Belief Propagation Guided Decimation on Random k-XORSAT}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{47:1--47:21},
  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.2025.47},
  URN =		{urn:nbn:de:0030-drops-234248},
  doi =		{10.4230/LIPIcs.ICALP.2025.47},
  annote =	{Keywords: random k-XORSAT, belief propagation, decimation process, random matrices}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.65
Analysing Survey Propagation Guided Decimationon Random Formulas

Authors: Samuel Hetterich

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
Let vec(theta) be a uniformly distributed random k-SAT formula with n variables and m clauses. For clauses/variables ratio m/n <= r_{k-SAT} ~ 2^k*ln(2) the formula vec(theta) is satisfiable with high probability. However, no efficient algorithm is known to provably find a satisfying assignment beyond m/n ~ 2k*ln(k)/k with a non-vanishing probability. Non-rigorous statistical mechanics work on k-CNF led to the development of a new efficient "message passing algorithm" called Survey Propagation Guided Decimation [Mézard et al., Science 2002]. Experiments conducted for k=3,4,5 suggest that the algorithm finds satisfying assignments close to r_{k-SAT}. However, in the present paper we prove that the basic version of Survey Propagation Guided Decimation fails to solve random k-SAT formulas efficiently already for m/n = 2^{k}(1 + epsilon_k)*ln(k)/k with lim_{k -> infinity} epsilon_k = 0 almost a factor k below r_{k-SAT}.
Cite as

Samuel Hetterich. Analysing Survey Propagation Guided Decimationon Random Formulas. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 65:1-65:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{hetterich:LIPIcs.ICALP.2016.65,
  author =	{Hetterich, Samuel},
  title =	{{Analysing Survey Propagation Guided Decimationon Random Formulas}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{65:1--65:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.65},
  URN =		{urn:nbn:de:0030-drops-62197},
  doi =		{10.4230/LIPIcs.ICALP.2016.65},
  annote =	{Keywords: Survey Propagation Guided Decimation, Message Passing Algorithm, Graph Theory, Random k-SAT}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.449
The Condensation Phase Transition in Random Graph Coloring

Authors: Victor Bapst, Amin Coja-Oghlan, Samuel Hetterich, Felicia Raßmann, and Dan Vilenchik

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
Based on a non-rigorous formalism called the "cavity method", physicists have put forward intriguing predictions on phase transitions in discrete structures. One of the most remarkable ones is that in problems such as random k-SAT or random graph k-coloring, very shortly before the threshold for the existence of solutions there occurs another phase transition called condensation [Krzakala et al., PNAS 2007]. The existence of this phase transition appears to be intimately related to the difficulty of proving precise results on, e.g., the k-colorability threshold as well as to the performance of message passing algorithms. In random graph k-coloring, there is a precise conjecture as to the location of the condensation phase transition in terms of a distributional fixed point problem. In this paper we prove this conjecture for k exceeding a certain constant k0.
Cite as

Victor Bapst, Amin Coja-Oghlan, Samuel Hetterich, Felicia Raßmann, and Dan Vilenchik. The Condensation Phase Transition in Random Graph Coloring. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 449-464, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{bapst_et_al:LIPIcs.APPROX-RANDOM.2014.449,
  author =	{Bapst, Victor and Coja-Oghlan, Amin and Hetterich, Samuel and Ra{\ss}mann, Felicia and Vilenchik, Dan},
  title =	{{The Condensation Phase Transition in Random Graph Coloring}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{449--464},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.449},
  URN =		{urn:nbn:de:0030-drops-47168},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.449},
  annote =	{Keywords: random graphs, graph coloring, phase transitions, message-passing algorithm}
}
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