LIPIcs.ICALP.2024.112.pdf
- Filesize: 0.86 MB
- 20 pages
Document
Testing Spreading Behavior in Networks with Arbitrary Topologies
Authors
Augusto Modanese 
,
Yuichi Yoshida
-
Part of:
Volume:
51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Colloquium on Automata, Languages, and Programming (ICALP) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-07-02
File
Document Identifiers
Author Details
Acknowledgements
We would like to thank Jukka Suomela for interesting discussions.
Cite AsGet BibTex
Augusto Modanese and Yuichi Yoshida. Testing Spreading Behavior in Networks with Arbitrary Topologies. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 112:1-112:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.112
https://doi.org/10.4230/LIPIcs.ICALP.2024.112
Abstract
Given the full topology of a network, how hard is it to test if it is evolving according to a local rule or is far from doing so? Inspired by the works of Goldreich and Ron (J. ACM, 2017) and Nakar and Ron (ICALP, 2021), we initiate the study of property testing in dynamic environments with arbitrary topologies. Our focus is on the simplest non-trivial rule that can be tested, which corresponds to the 1-BP rule of bootstrap percolation and models a simple spreading behavior: Every "infected" node stays infected forever, and each "healthy" node becomes infected if and only if it has at least one infected neighbor. Our results are subdivided into two main groups:
- If we are testing a single time step of evolution, then the query complexity is O(Δ/ε) or Õ(√n/ε) (whichever is smaller), where Δ and n are the maximum degree of a node and the number of vertices in the underlying graph, respectively. We also give lower bounds for both one- and two-sided error testers that match our upper bounds up to Δ = o(√n) and Δ = O(n^{1/3}), respectively. If ε is constant, then the first of these also holds against adaptive testers.
- When testing the environment over T time steps, we have two algorithms that need O(Δ^{T-1}/εT) and Õ(|E|/εT) queries, respectively, where E is the set of edges of the underlying graph. All of our algorithms are one-sided error, and all of them are also non-adaptive, with the single exception of the more complex Õ(√n/ε)-query tester for the case T = 2.
Subject Classification
ACM Subject Classification
- Theory of computation → Streaming, sublinear and near linear time algorithms
- Theory of computation → Distributed computing models
Keywords
- Property testing
- bootstrap percolation
- local phenomena
- expander graphs
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads
References
-
Noga Alon and Joel H. Spencer. The Probabilistic Method, Third Edition. Wiley-Interscience series in discrete mathematics and optimization. Wiley, 2008.
- József Balogh and Boris G. Pittel. Bootstrap percolation on the random regular graph. Random Struct. Algorithms, 30(1-2):257-286, 2007. URL: https://doi.org/10.1002/RSA.20158.
- Yair Bartal. Probabilistic approximations of metric spaces and its algorithmic applications. In Proceedings of the 37th Annual Symposium on Foundations of Computer Science (FOCS), pages 184-193, 1996. URL: https://doi.org/10.1109/SFCS.1996.548477.
- Arnab Bhattacharyya and Yuichi Yoshida. An algebraic characterization of testable boolean CSPs. In Proceedings of the 40th International Colloquium on Automata, Languages, and Programming (ICALP), volume 7965, pages 123-134, 2013. URL: https://doi.org/10.1007/978-3-642-39206-1_11.
- Arnab Bhattacharyya and Yuichi Yoshida. Property Testing - Problems and Techniques. Springer, 2022. URL: https://doi.org/10.1007/978-981-16-8622-1.
- Hubie Chen, Matt Valeriote, and Yuichi Yoshida. Constant-query testability of assignments to constraint satisfaction problems. SIAM J. Comput., 48(3):1022-1045, 2019. URL: https://doi.org/10.1137/18M121085X.
- Eldar Fischer, Eric Lehman, Ilan Newman, Sofya Raskhodnikova, Ronitt Rubinfeld, and Alex Samorodnitsky. Monotonicity testing over general poset domains. In Proceedings on 34th Annual ACM Symposium on Theory of Computing (STOC), pages 474-483, 2002. URL: https://doi.org/10.1145/509907.509977.
- Silvio Frischknecht, Barbara Keller, and Roger Wattenhofer. Convergence in (social) influence networks. In Proceedings of the 27th International Symposium on Distributed Computing (DISC), pages 433-446, 2013. URL: https://doi.org/10.1007/978-3-642-41527-2_30.
-
Oded Goldreich. Computational Complexity: A Conceptional Perspective. Cambridge University Press, 2008.
- Oded Goldreich and Dana Ron. On learning and testing dynamic environments. J. ACM, 64(3):21:1-21:90, 2017. URL: https://doi.org/10.1145/3088509.
- Paolo De Gregorio, Aonghus Lawlor, and Kenneth A. Dawson. Bootstrap percolation. In Robert A. Meyers, editor, Encyclopedia of Complexity and Systems Science, pages 608-626. Springer, 2009. URL: https://doi.org/10.1007/978-0-387-30440-3_41.
- Bernd Gärtner and Ahad N. Zehmakan. Majority model on random regular graphs. In Proceedings of the 13th Latin American Theoretical Informatics Symposium (LATIN), pages 572-583, 2018. URL: https://doi.org/10.1007/978-3-319-77404-6_42.
- Svante Janson, Tomasz Łuczak, Tatyana Turova, and Thomas Vallier. Bootstrap percolation on the random graph g_n,p. Ann. Appl. Probab., 22(5):1989-2047, 2012. URL: https://doi.org/10.1214/11-AAP822.
- Dominik Kaaser, Frederik Mallmann-Trenn, and Emanuele Natale. On the voting time of the deterministic majority process. In Proceedings of the 41st International Symposium on Mathematical Foundations of Computer Science (MFCS), pages 55:1-55:15, 2016. URL: https://doi.org/10.4230/LIPIcs.MFCS.2016.55.
- Philip N. Klein, Serge A. Plotkin, and Satish Rao. Excluded minors, network decomposition, and multicommodity flow. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing (STOC), pages 682-690, 1993. URL: https://doi.org/10.1145/167088.167261.
- Diego Maldonado, Pedro Montealegre, Martín Ríos Wilson, and Guillaume Theyssier. Local certification of majority dynamics. In Henning Fernau, Serge Gaspers, and Ralf Klasing, editors, SOFSEM 2024: Theory and Practice of Computer Science - 49th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2024, Cochem, Germany, February 19-23, 2024, Proceedings, volume 14519 of Lecture Notes in Computer Science, pages 369-382. Springer, 2024. URL: https://doi.org/10.1007/978-3-031-52113-3_26.
- Augusto Modanese and Yuichi Yoshida. Testing spreading behavior in networks with arbitrary topologies. CoRR, abs/2309.05442, 2023. URL: https://arxiv.org/abs/2309.05442.
- Yonatan Nakar and Dana Ron. Testing dynamic environments: Back to basics. In Proceedings of the 48th International Colloquium on Automata, Languages, and Programming (ICALP), pages 98:1-98:20, 2021. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.98.
- Salil P. Vadhan. Pseudorandomness. Found. Trends Theor. Comput. Sci., 7(1-3):1-336, 2012. URL: https://doi.org/10.1561/0400000010.
- Ahad N. Zehmakan. Tight bounds on the minimum size of a dynamic monopoly. In Proceedings of the 13th International Conference on Language and Automata Theory and Applications (LATA), pages 381-393, 2019. URL: https://doi.org/10.1007/978-3-030-13435-8_28.
- Ahad N. Zehmakan. Majority opinion diffusion in social networks: An adversarial approach. In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI), pages 5611-5619, 2021. URL: https://doi.org/10.1609/aaai.v35i6.16705.