Fraud Detection for Random Walks

Authors Varsha Dani, Thomas P. Hayes, Seth Pettie, Jared Saia

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Varsha Dani
  • Rochester Institute of Technology, Rochester, NY, USA
Thomas P. Hayes
  • University at Buffalo, Buffalo, NY, USA
Seth Pettie
  • University of Michigan, Ann Arbor, MI, USA
Jared Saia
  • University of New Mexico, Albuquerque, NM, USA

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Varsha Dani, Thomas P. Hayes, Seth Pettie, and Jared Saia. Fraud Detection for Random Walks. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Traditional fraud detection is often based on finding statistical anomalies in data sets and transaction histories. A sophisticated fraudster, aware of the exact kinds of tests being deployed, might be difficult or impossible to catch. We are interested in paradigms for fraud detection that are provably robust against any adversary, no matter how sophisticated. In other words, the detection strategy should rely on signals in the data that are inherent in the goals the adversary is trying to achieve. Specifically, we consider a fraud detection game centered on a random walk on a graph. We assume this random walk is implemented by having a player at each vertex, who can be honest or not. In particular, when the random walk reaches a vertex owned by an honest player, it proceeds to a uniformly random neighbor at the next timestep. However, when the random walk reaches a dishonest player, it instead proceeds to an arbitrary neighbor chosen by an omniscient Adversary. The game is played between the Adversary and a Referee who sees the trajectory of the random walk. At any point during the random walk, if the Referee determines that a {specific} vertex is controlled by a dishonest player, the Referee accuses that player, and therefore wins the game. The Referee is allowed to make the occasional incorrect accusation, but must follow a policy that makes such mistakes with small probability of error. The goal of the adversary is to make the cover time large, ideally infinite, i.e., the walk should never reach at least one vertex. We consider the following basic question: how much can the omniscient Adversary delay the cover time without getting caught? Our main result is a tight upper bound on this delay factor. We also discuss possible applications of our results to settings such as Rotor Walks, Leader Election, and Sybil Defense.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
  • Mathematics of computing → Probability and statistics
  • Security and privacy → Intrusion detection systems
  • Fraud detection
  • random processes
  • Markov chains


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