Document Open Access Logo

Streaming and Sketching Complexity of CSPs: A Survey (Invited Talk)

Author Madhu Sudan

PDF

File

Thumbnail PDF
PDF
LIPIcs.ICALP.2022.5.pdf
  • Filesize: 0.85 MB
  • 20 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Sketching and sampling
Keywords
  • Streaming algorithms
  • Sketching algorithms
  • Dichotomy
  • Communication Complexity

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

In this survey we describe progress over the last decade or so in understanding the complexity of solving constraint satisfaction problems (CSPs) approximately in the streaming and sketching models of computation. After surveying some of the results we give some sketches of the proofs and in particular try to explain why there is a tight dichotomy result for sketching algorithms working in subpolynomial space regime.

Cite As Get BibTex

Madhu Sudan. Streaming and Sketching Complexity of CSPs: A Survey (Invited Talk). In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ICALP.2022.5

Author Details

Madhu Sudan
  • School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

Funding

  • Sudan, Madhu: Supported in part by a Simons Investigator Award and NSF Awards CCF 1715187 and CCF 2152413.

Acknowledgements

I want to thank Santhoshini Velusamy for introducing me to this wonderful line of research. I want to thank her and all other co-authors - Chi-Ning Chou, Sasha Golovnev, Noah Singer, Raghuvansh Saxena, Amirbehshad Shahrasbi and Ameya Velingker - for the collaborations and discussions which informed this survey. They also caught numerous errors and gave suggestions that have hopefully made this survey more readable. I want to thank the organizers of ICALP 2022 for inviting me to write this survey, and to David Woodruff in particular for the additional encouragement and nudges that were crucial to get me going.

References

  1. Alexandr Andoni, Robert Krauthgamer, and Krzysztof Onak. Streaming Algorithms via Precision Sampling. In 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science (FOCS 2011, Palm Springs, CA, USA, October 23-25, 2011), pages 363-372, October 2011. URL: https://doi.org/10.1109/FOCS.2011.82.
  2. Sepehr Assadi, Gillat Kol, Raghuvansh R. Saxena, and Huacheng Yu. Multi-Pass Graph Streaming Lower Bounds for Cycle Counting, MAX-CUT, Matching Size, and Other Problems. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS 2020, Virtual, November 16-19, 2020), pages 354-364, November 2020. URL: https://doi.org/10.1109/FOCS46700.2020.00041.
  3. Sepehr Assadi and Vishvajeet N. Graph streaming lower bounds for parameter estimation and property testing via a streaming XOR lemma. In Samir Khuller and Virginia Vassilevska Williams, editors, STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual Event, Italy, June 21-25, 2021, pages 612-625. ACM, 2021. URL: https://doi.org/10.1145/3406325.3451110.
  4. Libor Barto and Marcin Kozik. Robust satisfiability of constraint satisfaction problems. In Howard J. Karloff and Toniann Pitassi, editors, Proceedings of the 44th Symposium on Theory of Computing Conference, STOC 2012, New York, NY, USA, May 19 - 22, 2012, pages 931-940. ACM, 2012. URL: https://doi.org/10.1145/2213977.2214061.
  5. Saugata Basu, Richard Pollack, and Marie-Françoise Roy. Algorithms in Real Algebraic Geometry. Springer, 2006. Google Scholar
  6. Joanna Boyland, Michael Hwang, Tarun Prasad, Noah Singer, and Santhoshini Velusamy. Closed-form expressions for the sketching approximability of (some) symmetric Boolean CSPs. CoRR, abs/2112.06319, 2021. URL: http://arxiv.org/abs/2112.06319.
  7. Andrei A. Bulatov. A Dichotomy Theorem for Nonuniform CSPs. In 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS 2017, Berkeley, CA, USA, October 15-17, 2017), pages 319-330, October 2017. URL: https://doi.org/10.1109/FOCS.2017.37.
  8. Jin-Yi Cai and Xi Chen. Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain. Cambridge University Press, 2017. Google Scholar
  9. Lijie Chen, Gillat Kol, Dmitry Paramonov, Raghuvansh Saxena, Zhao Song, and Huacheng Yu. Personal communication, March 2021. Google Scholar
  10. Chi-Ning Chou, Alexander Golovnev, Amirbehshad Shahrasbi, Madhu Sudan, and Santhoshini Velusamy. Sketching approximability of (weak) monarchy predicates. Manuscript, May 2022. Google Scholar
  11. Chi-Ning Chou, Alexander Golovnev, Madhu Sudan, Ameya Velingker, and Santhoshini Velusamy. Linear space streaming lower bounds for approximating CSPs. CoRR, abs/2106.13078, 2021. Extended abstract in Proc. STOC 2022. URL: http://arxiv.org/abs/2106.13078.
  12. Chi-Ning Chou, Alexander Golovnev, Madhu Sudan, and Santhoshini Velusamy. Approximability of all Boolean CSPs with linear sketches. CoRR, abs/2102.12351, 2021. URL: http://arxiv.org/abs/2102.12351.
  13. Chi-Ning Chou, Alexander Golovnev, Madhu Sudan, and Santhoshini Velusamy. Approximability of all finite CSPs with linear sketches. CoRR, abs/2105.01161, 2021. Extended abstract appears in Proc. FOCS 2021. URL: http://arxiv.org/abs/2105.01161.
  14. Chi-Ning Chou, Alexander Golovnev, and Santhoshini Velusamy. Optimal Streaming Approximations for all Boolean Max-2CSPs and Max-kSAT. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS 2020, Virtual, November 16-19, 2020), pages 330-341. IEEE Computer Society, November 2020. URL: https://doi.org/10.1109/FOCS46700.2020.00039.
  15. Nadia Creignou, Sanjeev Khanna, and Madhu Sudan. Complexity Classifications of Boolean Constraint Satisfaction Problems. Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics, 2001. URL: https://doi.org/10.1137/1.9780898718546.
  16. Víctor Dalmau and Andrei A. Krokhin. Robust satisfiability for CSPs: Hardness and algorithmic results. ACM Trans. Comput. Theory, 5(4):15:1-15:25, 2013. URL: https://doi.org/10.1145/2540090.
  17. Tomás Feder and Moshe Y. Vardi. The computational structure of monotone monadic SNP and constraint satisfaction: A study through datalog and group theory. SIAM J. Comput., 28(1):57-104, 1998. URL: https://doi.org/10.1137/S0097539794266766.
  18. Dmitry Gavinsky, Julia Kempe, Iordanis Kerenidis, Ran Raz, and Ronald de Wolf. Exponential separation for one-way quantum communication complexity, with applications to cryptography. SIAM Journal on Computing, 38(5):1695-1708, December 2008. Conference version in STOC 2007. URL: https://doi.org/10.1137/070706550.
  19. Venkatesan Guruswami, Ameya Velingker, and Santhoshini Velusamy. Streaming Complexity of Approximating Max 2CSP and Max Acyclic Subgraph. In Klaus Jansen, José D. P. Rolim, David Williamson, and Santosh S. Vempala, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2017, Berkeley, CA, USA, August 16-18, 2017), volume 81 of LIPIcs, pages 8:1-8:19. Schloss Dagstuhl emdash Leibniz-Zentrum für Informatik, August 2017. URL: https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2017.8.
  20. Piotr Indyk. Stable distributions, pseudorandom generators, embeddings, and data stream computation. Journal of the ACM, 53(3):307-323, May 2006. Conference version in FOCS 2000. URL: https://doi.org/10.1145/1147954.1147955.
  21. Piotr Indyk, Andrew McGregor, Ilan Newman, and Krzysztof Onak. Open problems in data streams, property testing, and related topics, June 2011. Compiled from IITK Workshop on Algorithms for Processing Massive Data Sets (2009) and Bertinoro Workshop on Sublinear Algorithms (2011). Google Scholar
  22. Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. Streaming lower bounds for approximating MAX-CUT. In Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2015, San Diego, California, USA, January 4-6, 2015), pages 1263-1282. Society for Industrial and Applied Mathematics, January 2015. URL: https://doi.org/10.1137/1.9781611973730.84.
  23. Michael Kapralov, Sanjeev Khanna, Madhu Sudan, and Ameya Velingker. (1 + ω(1))-approximation to MAX-CUT requires linear space. In Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017, Barcelona, Spain, January 16-19, 2017), pages 1703-1722. Society for Industrial and Applied Mathematics, January 2017. URL: https://doi.org/10.5555/3039686.3039798.
  24. Michael Kapralov and Dmitry Krachun. An optimal space lower bound for approximating MAX-CUT. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (STOC 2019, Phoenix, AZ, USA, June 23-26, 2019), pages 277-288. Association for Computing Machinery, June 2019. URL: https://doi.org/10.1145/3313276.3316364.
  25. Sanjeev Khanna, Madhu Sudan, Luca Trevisan, and David P. Williamson. The Approximability of Constraint Satisfaction Problems. SIAM Journal on Computing, 30(6):1863-1920, January 2001. Conference versions in STOC 1997 and CCC 1997. URL: https://doi.org/10.1137/S0097539799349948.
  26. Dmitry Kogan and Robert Krauthgamer. Sketching cuts in graphs and hypergraphs. In Proceedings of the 6th Annual Conference on Innovations in Theoretical Computer Science (ITCS 2015, Rehovot, Israel, January 11-13, 2015), pages 367-376. Association for Computing Machinery, 2015. URL: https://doi.org/10.1145/2688073.2688093.
  27. Gábor Kun, Ryan O'Donnell, Suguru Tamaki, Yuichi Yoshida, and Yuan Zhou. Linear programming, width-1 CSPs, and robust satisfaction. In Shafi Goldwasser, editor, Innovations in Theoretical Computer Science 2012, Cambridge, MA, USA, January 8-10, 2012, pages 484-495. ACM, 2012. URL: https://doi.org/10.1145/2090236.2090274.
  28. Prasad Raghavendra. Optimal algorithms and inapproximability results for every CSP? In Proceedings of the 40th Annual ACM Symposium on Theory of Computing (STOC 2008, Victoria, BC, Canada, May 17-20, 2008), pages 245-254, 2008. URL: https://doi.org/10.1145/1374376.1374414.
  29. Thomas J. Schaefer. The complexity of satisfiability problems. In Proceedings of the 10th Annual ACM Symposium on Theory of Computing (STOC 1978, San Diego, CA, USA, May 1-May 3, 1978), pages 216-226. Association for Computing Machinery, May 1978. URL: https://doi.org/10.1145/800133.804350.
  30. Noah Singer, Madhu Sudan, and Santhoshini Velusamy. Streaming approximation resistance of every ordering CSP. In Mary Wootters and Laura Sanità, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2021, August 16-18, 2021), volume 207 of LIPIcs, pages 17:1-17:19. Schloss Dagstuhl emdash Leibniz-Zentrum für Informatik, September 2021. URL: https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.17.
  31. Dmitriy Zhuk. A Proof of the CSP Dichotomy Conjecture. Journal of the ACM, 67(5):30:1-30:78, August 2020. Conference version in FOCS 2017. URL: https://doi.org/10.1145/3402029.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact