Document Open Access Logo

Lower Bounds for Subgraph Detection in the CONGEST Model

Authors Tzlil Gonen, Rotem Oshman



PDF
Thumbnail PDF

File

LIPIcs.OPODIS.2017.6.pdf
  • Filesize: 0.57 MB
  • 16 pages

Document Identifiers

Author Details

Tzlil Gonen
Rotem Oshman

Cite AsGet BibTex

Tzlil Gonen and Rotem Oshman. Lower Bounds for Subgraph Detection in the CONGEST Model. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 6:1-6:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.OPODIS.2017.6

Abstract

In the subgraph-freeness problem, we are given a constant-sized graph H, and wish to de- termine whether the network graph contains H as a subgraph or not. Until now, the only lower bounds on subgraph-freeness known for the CONGEST model were for cycles of length greater than 3; here we extend and generalize the cycle lower bound, and obtain polynomial lower bounds for subgraph-freeness in the CONGEST model for two classes of subgraphs. The first class contains any graph obtained by starting from a 2-connected graph H for which we already know a lower bound, and replacing the vertices of H by arbitrary connected graphs. We show that the lower bound on H carries over to the new graph. The second class is constructed by starting from a cycle Ck of length k ≥ 4, and constructing a graph H ̃ from Ck by replacing each edge {i, (i + 1) mod k} of the cycle with a connected graph Hi, subject to some constraints on the graphs H_{0}, . . . , H_{k−1}. In this case we obtain a polynomial lower bound for the new graph H ̃, depending on the size of the shortest cycle in H ̃ passing through the vertices of the original k-cycle.
Keywords
  • subgraph freeness
  • CONGEST
  • lower bounds

Metrics

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

References

  1. Amir Abboud, Keren Censor-Hillel, Seri Khoury, and Christoph Lenzen. Fooling views: A new lower bound technique for distributed computations under congestion. CoRR, abs/1711.01623, 2017. Google Scholar
  2. Noga Alon, Raphael Yuster, and Uri Zwick. Color-coding. J. ACM, 42(4):844-856, 1995. Google Scholar
  3. Zvika Brakerski and Boaz Patt-Shamir. Distributed discovery of large near-cliques. Distributed Computing, 24(2):79-89, 2011. Google Scholar
  4. Keren Censor-Hillel, Eldar Fischer, Gregory Schwartzman, and Yadu Vasudev. Fast Distributed Algorithms for Testing Graph Properties, pages 43-56. Springer, Berlin, Heidelberg, 2016. URL: http://dx.doi.org/10.1007/978-3-662-53426-7_4.
  5. Keren Censor-Hillel, Petteri Kaski, Janne H. Korhonen, Christoph Lenzen, Ami Paz, and Jukka Suomela. Algebraic methods in the congested clique. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, PODC 2015, pages 143-152, 2015. Google Scholar
  6. Danny Dolev, Christoph Lenzen, and Shir Peled. "Tri, Tri Again": Finding Triangles and Small Subgraphs in a Distributed Setting, pages 195-209. Springer, Berlin, Heidelberg, 2012. URL: http://dx.doi.org/10.1007/978-3-642-33651-5_14.
  7. Andrew Drucker, Fabian Kuhn, and Rotem Oshman. On the power of the congested clique model. In Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing, PODC '14, pages 367-376, 2014. Google Scholar
  8. Guy Even, Orr Fischer, Pierre Fraigniaud, Tzlil Gonen, Reut Levi, Moti Medina, Pedro Montealegre, Dennis Olivetti, Rotem Oshman, Ivan Rapaport, and Ioan Todinca. Three Notes on Distributed Property Testing. In 31st International Symposium on Distributed Computing (DISC 2017), volume 91 of Leibniz International Proceedings in Informatics (LIPIcs), pages 15:1-15:30, 2017. Google Scholar
  9. Guy Even, Reut Levi, and Moti Medina. Faster and simpler distributed algorithms for testing and correcting graph properties in the congest-model. CoRR, abs/1705.04898, 2017. Google Scholar
  10. Orr Fischer, Tzlil Gonen, and Rotem Oshman. Distributed property testing for subgraph-freeness revisited. CoRR, abs/1705.04033, 2017. Google Scholar
  11. Pierre Fraigniaud, Pedro Montealegre, Dennis Olivetti, Ivan Rapaport, and Ioan Todinca. Distributed subgraph detection. CoRR, abs/1706.03996, 2017. Google Scholar
  12. Pierre Fraigniaud, Ivan Rapaport, Ville Salo, and Ioan Todinca. Distributed Testing of Excluded Subgraphs, pages 342-356. Springer, Berlin, Heidelberg, 2016. URL: http://dx.doi.org/10.1007/978-3-662-53426-7_25.
  13. Eugene C. Freuder. A sufficient condition for backtrack-bounded search. J. ACM, 32(4):755-761, 1985. Google Scholar
  14. Zoltán Füredi and Miklós Simonovits. The History of Degenerate (Bipartite) Extremal Graph Problems, pages 169-264. Springer, Berlin, Heidelberg, 2013. Google Scholar
  15. Taisuke Izumi and François Le Gall. Triangle finding and listing in congest networks. In Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC '17, pages 381-389, 2017. Google Scholar
  16. Bala Kalyanasundaram and Georg Schnitger. The probabilistic communication complexity of set intersection. SIAM J. Discrete Math., 5(4):545-557, 1992. Google Scholar
  17. Janne H. Korhonen and Joel Rybicki. Deterministic subgraph detection in broadcast CONGEST. CoRR, abs/1705.10195, 2017. Google Scholar
  18. Eyal Kushilevitz and Noam Nisan. Communication Complexity. Cambridge University Press, 1997. Google Scholar
  19. Felix Lazebnik, Vasiliy A. Ustimenko, and Andrew J. Woldar. A new series of dense graphs of high girth. Bull. Amer. Math. Soc., 32(1):73-39, 1995. Google Scholar
  20. Alexander A. Razborov. On the distributional complexity of disjointness. Theor. Comput. Sci., 106(2):385-390, 1992. Google Scholar
  21. J. R. Ullmann. An algorithm for subgraph isomorphism. J. ACM, 23(1):31-42, 1976. Google Scholar
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