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Being Corrupt Requires Being Clever, But Detecting Corruption Doesn't

Authors Yan Jin, Elchanan Mossel, Govind Ramnarayan

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Author Details

Yan Jin
  • MIT, 77 Massachusetts Ave, MA, USA
Elchanan Mossel
  • MIT, 77 Massachusetts Ave, MA, USA
Govind Ramnarayan
  • MIT, 77 Massachusetts Ave, MA, USA

Funding

  • Jin, Yan: Partially supported by Institute for Data, Systems and Society Fellowship.
  • Mossel, Elchanan: Partially supported by awards ONR N00014-16-1-2227, NSF CCF1665252 and DMS-1737944.
  • Ramnarayan, Govind: Partially supported by awards NSF CCF 1665252 and DMS-1737944.

Cite As Get BibTex

Yan Jin, Elchanan Mossel, and Govind Ramnarayan. Being Corrupt Requires Being Clever, But Detecting Corruption Doesn't. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 45:1-45:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ITCS.2019.45

Abstract

We consider a variation of the problem of corruption detection on networks posed by Alon, Mossel, and Pemantle '15. In this model, each vertex of a graph can be either truthful or corrupt. Each vertex reports about the types (truthful or corrupt) of all its neighbors to a central agency, where truthful nodes report the true types they see and corrupt nodes report adversarially. The central agency aggregates these reports and attempts to find a single truthful node. Inspired by real auditing networks, we pose our problem for arbitrary graphs and consider corruption through a computational lens. We identify a key combinatorial parameter of the graph m(G), which is the minimal number of corrupted agents needed to prevent the central agency from identifying a single corrupt node. We give an efficient (in fact, linear time) algorithm for the central agency to identify a truthful node that is successful whenever the number of corrupt nodes is less than m(G)/2. On the other hand, we prove that for any constant alpha > 1, it is NP-hard to find a subset of nodes S in G such that corrupting S prevents the central agency from finding one truthful node and |S| <= alpha m(G), assuming the Small Set Expansion Hypothesis (Raghavendra and Steurer, STOC '10). We conclude that being corrupt requires being clever, while detecting corruption does not.
Our main technical insight is a relation between the minimum number of corrupt nodes required to hide all truthful nodes and a certain notion of vertex separability for the underlying graph. Additionally, this insight lets us design an efficient algorithm for a corrupt party to decide which graphs require the fewest corrupted nodes, up to a multiplicative factor of O(log n).

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Corruption detection
  • PMC Model
  • Small Set Expansion
  • Hardness of Approximation

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References

  1. Noga Alon, Elchanan Mossel, and Robin Pemantle. Corruption Detection on Networks. CoRR, abs/1505.05637, 2015. URL: http://arxiv.org/abs/1505.05637.
  2. Per Austrin, Toniann Pitassi, and Yu Wu. Inapproximability of Treewidth, One-Shot Pebbling, and Related Layout Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Cambridge, MA, USA, August 15-17, 2012. Proceedings, pages 13-24, 2012. URL: http://dx.doi.org/10.1007/978-3-642-32512-0_2.
  3. Walid Ben-Ameur, Mohamed-Ahmed Mohamed-Sidi, and José Neto. The k -separator problem: polyhedra, complexity and approximation results. J. Comb. Optim., 29(1):276-307, 2015. URL: http://dx.doi.org/10.1007/s10878-014-9753-x.
  4. Hans L. Bodlaender, John R. Gilbert, Hjálmtyr Hafsteinsson, and Ton Kloks. Approximating Treewidth, Pathwidth, Frontsize, and Shortest Elimination Tree. J. Algorithms, 18(2):238-255, 1995. Google Scholar
  5. Anton T. Dahbura and Gerald M. Masson. An O(n^2.5) Fault Identification Algorithm for Diagnosable Systems. IEEE Trans. Computers, 33(6):486-492, 1984. URL: http://dx.doi.org/10.1109/TC.1984.1676472.
  6. Odd-Helge Fjeldstad. Fighting fiscal corruption: lessons from the Tanzania Revenue Authority. Public Administration and Development: The International Journal of Management Research and Practice, 23(2):165-175, 2003. Google Scholar
  7. S. Louis Hakimi and A. T. Amin. Characterization of Connection Assignment of Diagnosable Systems. IEEE Trans. Computers, 23(1):86-88, 1974. URL: http://dx.doi.org/10.1109/T-C.1974.223782.
  8. Yan Jin, Elchanan Mossel, and Govind Ramnarayan. Being Corrupt Requires Being Clever, But Detecting Corruption Doesn't. arXiv, 2018. URL: http://arxiv.org/abs/1809.10325.
  9. Tiko Kameda, S Toida, and FJ Allan. A diagnosing algorithm for networks. Information and Control, 29(2):141-148, 1975. Google Scholar
  10. David Kempe, Jon M. Kleinberg, and Éva Tardos. Maximizing the Spread of Influence through a Social Network. Theory of Computing, 11:105-147, 2015. URL: http://dx.doi.org/10.4086/toc.2015.v011a004.
  11. Subhash Khot. On the Power of Unique 2-Prover 1-Round Games. In Proceedings of the 17th Annual IEEE Conference on Computational Complexity, Montréal, Québec, Canada, May 21-24, 2002, page 25, 2002. URL: http://dx.doi.org/10.1109/CCC.2002.1004334.
  12. Jon G Kuhl and Sudhakar M Reddy. Distributed fault-tolerance for large multiprocessor systems. In Proceedings of the 7th annual symposium on Computer Architecture, pages 23-30. ACM, 1980. Google Scholar
  13. Euiwoong Lee. Partitioning a Graph into Small Pieces with Applications to Path Transversal. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 1546-1558, 2017. URL: http://dx.doi.org/10.1137/1.9781611974782.101.
  14. Shachindra N. Maheshwari and S. Louis Hakimi. On Models for Diagnosable Systems and Probabilistic Fault Diagnosis. IEEE Trans. Computers, 25(3):228-236, 1976. Google Scholar
  15. Thebeth Rufaro Mukwembi and Simon Mukwembi. Corruption and its detection: a graph-theoretic approach. Computational and Mathematical Organization Theory, 23(2):293-300, June 2017. URL: http://dx.doi.org/10.1007/s10588-016-9227-z.
  16. Richard P Nielsen. Corruption networks and implications for ethical corruption reform. Journal of Business ethics, 42(2):125-149, 2003. Google Scholar
  17. Maarten Oosten, Jeroen HGC Rutten, and Frits CR Spieksma. Disconnecting graphs by removing vertices: a polyhedral approach. Statistica Neerlandica, 61(1):35-60, 2007. Google Scholar
  18. Franco P. Preparata, Gernot Metze, and Robert T. Chien. On the Connection Assignment Problem of Diagnosable Systems. IEEE Trans. Electronic Computers, 16(6):848-854, 1967. URL: http://dx.doi.org/10.1109/PGEC.1967.264748.
  19. Prasad Raghavendra and David Steurer. Graph expansion and the unique games conjecture. In Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010, Cambridge, Massachusetts, USA, 5-8 June 2010, pages 755-764, 2010. URL: http://dx.doi.org/10.1145/1806689.1806788.
  20. Prasad Raghavendra, David Steurer, and Madhur Tulsiani. Reductions between Expansion Problems. In Proceedings of the 27th Conference on Computational Complexity, CCC 2012, Porto, Portugal, June 26-29, 2012, pages 64-73, 2012. URL: http://dx.doi.org/10.1109/CCC.2012.43.
  21. Gregory F. Sullivan. A Polynomial Time Algorithm for Fault Diagnosability. In FOCS, pages 148-156. IEEE Computer Society, 1984. Google Scholar
  22. Jie Xu and Shi-ze Huang. Sequentially t-Diagnosable Systems: A Characterization and Its Applications. IEEE Trans. Computers, 44(2):340-345, 1995. URL: http://dx.doi.org/10.1109/12.364544.
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