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Documents authored by Anand, Konrad

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.11
Approximate Counting for Spin Systems in Sub-Quadratic Time

Authors: Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, and Jiaheng Wang

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We present two randomised approximate counting algorithms with Õ(n^{2-c}/ε²) running time for some constant c > 0 and accuracy ε: 1) for the hard-core model with fugacity λ on graphs with maximum degree Δ when λ = O(Δ^{-1.5-c₁}) where c₁ = c/(2-2c); 2) for spin systems with strong spatial mixing (SSM) on planar graphs with quadratic growth, such as ℤ². For the hard-core model, Weitz’s algorithm (STOC, 2006) achieves sub-quadratic running time when correlation decays faster than the neighbourhood growth, namely when λ = o(Δ^{-2}). Our first algorithm does not require this property and extends the range where sub-quadratic algorithms exist. Our second algorithm appears to be the first to achieve sub-quadratic running time up to the SSM threshold, albeit on a restricted family of graphs. It also extends to (not necessarily planar) graphs with polynomial growth, such as ℤ^d, but with a running time of the form Õ(n²ε^{-2}/2^{c(log n)^{1/d}}) where d is the exponent of the polynomial growth and c > 0 is some constant.
Cite as

Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, and Jiaheng Wang. Approximate Counting for Spin Systems in Sub-Quadratic Time. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{anand_et_al:LIPIcs.ICALP.2024.11,
  author =	{Anand, Konrad and Feng, Weiming and Freifeld, Graham and Guo, Heng and Wang, Jiaheng},
  title =	{{Approximate Counting for Spin Systems in Sub-Quadratic Time}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.11},
  URN =		{urn:nbn:de:0030-drops-201543},
  doi =		{10.4230/LIPIcs.ICALP.2024.11},
  annote =	{Keywords: Randomised algorithm, Approximate counting, Spin system, Sub-quadratic algorithm}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.38
Perfect Sampling for Hard Spheres from Strong Spatial Mixing

Authors: Konrad Anand, Andreas Göbel, Marcus Pappik, and Will Perkins

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
We provide a perfect sampling algorithm for the hard-sphere model on subsets of R^d with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling algorithms have been devised to sample from the hard-sphere model, and our perfect sampling algorithm is efficient for a range of parameters for which only efficient approximate samplers were previously known and is faster than these known approximate approaches. Our methods also extend to the more general setting of Gibbs point processes interacting via finite-range, repulsive potentials.
Cite as

Konrad Anand, Andreas Göbel, Marcus Pappik, and Will Perkins. Perfect Sampling for Hard Spheres from Strong Spatial Mixing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 38:1-38:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{anand_et_al:LIPIcs.APPROX/RANDOM.2023.38,
  author =	{Anand, Konrad and G\"{o}bel, Andreas and Pappik, Marcus and Perkins, Will},
  title =	{{Perfect Sampling for Hard Spheres from Strong Spatial Mixing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{38:1--38:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.38},
  URN =		{urn:nbn:de:0030-drops-188638},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.38},
  annote =	{Keywords: perfect sampling, hard-sphere model, Gibbs point processes}
}
Document
DOI: 10.4230/DagRep.12.11.124
Counting and Sampling: Algorithms and Complexity (Dagstuhl Seminar 22482)

Authors: Holger Dell, Mark R. Jerrum, Haiko Müller, Konrad Anand, and Marcus Pappik

Published in: Dagstuhl Reports, Volume 12, Issue 11 (2023)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 22482 "Counting and Sampling: Algorithms and Complexity". We document the talks presented, covering many advances in the area made over the last five years. As well, we document the progress made by working groups on future projects.
Cite as

Holger Dell, Mark R. Jerrum, Haiko Müller, Konrad Anand, and Marcus Pappik. Counting and Sampling: Algorithms and Complexity (Dagstuhl Seminar 22482). In Dagstuhl Reports, Volume 12, Issue 11, pp. 124-145, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{dell_et_al:DagRep.12.11.124,
  author =	{Dell, Holger and Jerrum, Mark R. and M\"{u}ller, Haiko and Anand, Konrad and Pappik, Marcus},
  title =	{{Counting and Sampling: Algorithms and Complexity (Dagstuhl Seminar 22482)}},
  pages =	{124--145},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{12},
  number =	{11},
  editor =	{Dell, Holger and Jerrum, Mark R. and M\"{u}ller, Haiko and Anand, Konrad and Pappik, Marcus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.12.11.124},
  URN =		{urn:nbn:de:0030-drops-178394},
  doi =		{10.4230/DagRep.12.11.124},
  annote =	{Keywords: Sampling, Counting, Algorithms, Complexity, Statistical Physics, Phase Transitions, Markov Chains, Graphs, Point Processes}
}
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