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Sample-Based Distance-Approximation for Subsequence-Freeness

Authors Omer Cohen Sidon, Dana Ron

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LIPIcs.ICALP.2023.44.pdf
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Author Details

Omer Cohen Sidon
  • Tel Aviv University, Israel
Dana Ron
  • Tel Aviv University, Israel

Funding

  • Ron, Dana: Supported by the Israel Science Foundation (grant number 1146/18) and the Kadar-family award.

Cite AsGet BibTex

Omer Cohen Sidon and Dana Ron. Sample-Based Distance-Approximation for Subsequence-Freeness. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICALP.2023.44

Abstract

In this work, we study the problem of approximating the distance to subsequence-freeness in the sample-based distribution-free model. For a given subsequence (word) w = w_1 … w_k, a sequence (text) T = t_1 … t_n is said to contain w if there exist indices 1 ≤ i_1 < … < i_k ≤ n such that t_{i_{j}} = w_j for every 1 ≤ j ≤ k. Otherwise, T is w-free. Ron and Rosin (ACM TOCT 2022) showed that the number of samples both necessary and sufficient for one-sided error testing of subsequence-freeness in the sample-based distribution-free model is Θ(k/ε). Denoting by Δ(T,w,p) the distance of T to w-freeness under a distribution p:[n] → [0,1], we are interested in obtaining an estimate Δ̂, such that |Δ̂ - Δ(T,w,p)| ≤ δ with probability at least 2/3, for a given distance parameter δ. Our main result is an algorithm whose sample complexity is Õ(k²/δ²). We first present an algorithm that works when the underlying distribution p is uniform, and then show how it can be modified to work for any (unknown) distribution p. We also show that a quadratic dependence on 1/δ is necessary.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Property Testing
  • Distance Approximation

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References

  1. Nir Ailon, Bernard Chazelle, Seshadhri Comandur, and Ding Liu. Estimating the distance to a monotone function. Random Structures and Algorithms, 31(3):371-383, 2007. Google Scholar
  2. Ziv Bar-Yossef. Sampling lower bounds via information theory. In Proceedings of the 35th Annual ACM Symposium on the Theory of Computing, pages 335-344, 2003. Google Scholar
  3. Omri Ben-Eliezer, Eldar Fischer, Amit Levi, and Ron D. Rothblum. Hard properties with (very) short PCPPs and their applications. In Proceedings of the 11th Innovations in Theoretical Computer Science conference (ITCS), pages 9:1-9:27, 2020. Google Scholar
  4. Piotr Berman, Meiram Murzabulatov, and Sofya Raskhodnikova. Tolerant testers of image properties. ACM Transactions on Algorithms, 18(4):1-39, 2022. Article number 37. Google Scholar
  5. Piotr Berman, Sofya Raskhodnikova, and Grigory Yaroslavtsev. Lp-testing. In Proceedings of the 46th Annual ACM Symposium on the Theory of Computing, pages 164-173, 2014. Google Scholar
  6. Hadley Black, Deeparnab Chakrabarty, and C. Seshadhri. Domain reduction for monotonicity testing: A o(d) tester for boolean functions in d-dimensions. In Proceedings of the 31st Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1975-1994, 2020. Google Scholar
  7. Eric Blais, Clément L Canonne, Talya Eden, Amit Levi, and Dana Ron. Tolerant junta testing and the connection to submodular optimization and function isomorphism. ACM Transactions on Computation Theory, 11(4):1-33, 2019. Google Scholar
  8. Eric Blais, Renato Ferreira Pinto Jr., and Nathaniel Harms. VC dimension and distribution-free sample-based testing. In Proceedings of the 53rd Annual ACM Symposium on the Theory of Computing, pages 504-517, 2021. Google Scholar
  9. Avrim Blum and Lunjia Hu. Active tolerant testing. In Proceedings of the 31st Conference on Computational Learning Theory (COLT), pages 474-497, 2018. Google Scholar
  10. Mark Braverman, Subhash Khot, Guy Kindler, and Dor Minzer. Improved monotonicity testers via hypercube embeddings. In Proceedings of the 13th Innovations in Theoretical Computer Science conference (ITCS), pages 25:1-25:24, 2024. Google Scholar
  11. Andrea Campagna, Alan Guo, and Ronitt Rubinfeld. Local reconstructors and tolerant testers for connectivity and diameter. In Proceedings of the 17th International Workshop on Randomization and Computation, pages 411-424, 2013. Google Scholar
  12. Clément L Canonne, Elena Grigorescu, Siyao Guo, Akash Kumar, and Karl Wimmer. Testing k-monotonicity: The rise and fall of boolean functions. Theory of Computing, 15(1):1-55, 2019. This paper appeared in the proceedings of ITCS 2017. Google Scholar
  13. Omer Cohen Sidon. Sample-based distance-approximation for subsequence-freeness. MSc thesis, Tel Aviv University, 2023. Google Scholar
  14. Omer Cohen Sidon and Dana Ron. Sample-based distance-approximation for subsequence-freeness. arXiv preprint, 2023. URL: https://arxiv.org/abs/2305.01358.
  15. Ilias Diakonikolas and Daniel Kane. A new approach for testing properties of discrete distributions. In Proceedings of the 56th Annual IEEE Symposium on Foundations of Computer Science, pages 685-694, 2016. Google Scholar
  16. Shahar Fattal and Dana Ron. Approximating the distance to monotonicity in high dimensions. ACM Transactions on Algorithms, 6(3):1-37, 2010. Google Scholar
  17. Nimrod Fiat and Dana Ron. On efficient distance approximation for graph properties. In Proceedings of the 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1618-1637, 2021. Google Scholar
  18. Eldar Fischer and Lance Fortnow. Tolerant versus intolerant testing for boolean properties. Theory of Computing, 2:173-183, 2006. Google Scholar
  19. Eldar Fischer and Ilan Newman. Testing versus estimation of graph properties. SIAM Journal on Computing, 37(2):482-501, 2007. Google Scholar
  20. Oded Goldreich, Shafi Goldwasser, and Dana Ron. Property testing and its connections to learning and approximation. Journal of the ACM, 45:653-750, 1998. Google Scholar
  21. Venkat Guruswami and Atri Rudra. Tolerant locally testable codes. In Proceedings of the 9th International Workshop on Randomization and Computation, pages 306-317, 2005. Google Scholar
  22. Nathaniel Harms and Yuichi Yoshida. Downsampling for testing and learning in product distributions, 2022. Google Scholar
  23. Carlos Hoppen, Yoshiharu Kohayakawa, Richard Lang, Hanno Lefmann, and Henrique Stagni. Estimating the distance to a hereditary graph property. Electronic Notes in Discrete Mathematics, 61:607-613, 2017. Google Scholar
  24. Swastik Kopparty and Shubhangi Saraf. Tolerant linearity testing and locally testable codes. In Proceedings of the 13th International Workshop on Randomization and Computation, pages 601-614, 2009. Google Scholar
  25. Amit Levi and Erik Waingarten. Lower bounds for tolerant junta and unateness testing via rejection sampling of graphs. In Proceedings of the 10th Innovations in Theoretical Computer Science conference (ITCS), pages 52:1-52:20, 2019. Google Scholar
  26. Sharon Marko and Dana Ron. Distance approximation in bounded-degree and general sparse graphs. Transactions on Algorithms, 5(2), 2009. Article number 22. Google Scholar
  27. Ilan Newman and Nithin Varma. New sublinear algorithms and lower bounds for LIS estimation. In Automata, Languages and Programming: 48th International Colloquium, pages 100:1-100:20, 2021. Google Scholar
  28. Ramesh Krishnan S Pallavoor, Sofya Raskhodnikova, and Erik Waingarten. Approximating the distance to monotonicity of boolean functions. Random Structures & Algorithms, 60(2):233-260, 2022. Google Scholar
  29. Michal Parnas, Dana Ron, and Ronitt Rubinfeld. Tolerant property testing and distance approximation. Journal of Computer and System Sciences, 72(6):1012-1042, 2006. Google Scholar
  30. Dana Ron and Asaf Rosin. Optimal distribution-free sample-based testing of subsequence-freeness with one-sided error. ACM Transactions on Computation Theory, 14(4):1-31, 2022. An extended abstract of this work appeared in the proceedings of SODA 2021. Google Scholar
  31. Ronitt Rubinfeld and Madhu Sudan. Robust characterization of polynomials with applications to program testing. SIAM Journal on Computing, 25(2):252-271, 1996. Google Scholar
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