Differentially Private Triangle and 4-Cycle Counting in the Shuffle Model

Introduction

• The challenge of counting triangles and 4-cycles in a graph while safeguarding the privacy of individuals.
• Existing solutions predominantly rely on a central model, where a trusted third party collects and processes data.
• The shuffle model emerges as an alternative, distributing data among multiple servers and enabling computations on shuffled data without exposing individual information.

Shuffle Model

• The shuffle model operates in three phases: shuffle, computation, and unshuffle.
• In the shuffle phase, data is randomly shuffled across the servers.
• The computation phase involves each server performing calculations on the shuffled data.
• The unshuffle phase combines the results from individual servers to obtain the final outcome.

Differential Privacy

• Differential privacy is a privacy guarantee ensuring that computational outputs do not reveal information about individual data.
• A randomized algorithm is deemed differentially private if its output remains largely unaffected when an individual's data is removed from the input.

Differentially Private Triangle Counting

• The objective is to estimate the number of triangles in a graph while preserving individual privacy.
• The algorithm involves adding noise to the triangle count on each server during the computation phase.
• The noise addition adheres to differential privacy principles.
• The noise is removed in the unshuffle phase to arrive at the final result.

Differentially Private 4-Cycle Counting

• The aim is to estimate the number of 4-cycles in a graph while safeguarding individual privacy.
• The algorithm adds noise to the 4-cycle count on each server during the computation phase.
• The noise is added in a way that satisfies differential privacy requirements.
• The noise is removed in the unshuffle phase to obtain the final result.

Experimental Results

• The authors conducted experiments on real-world and synthetic datasets to assess the performance of the proposed algorithms.
• Results indicate that the algorithms effectively preserve privacy while accurately counting triangles and 4-cycles.
• The algorithms also outperform previous solutions in terms of runtime and communication complexity.

Conclusion

• The shuffle model provides an alternative approach for maintaining privacy in graph computations.
• The presented algorithms for differentially private triangle and 4-cycle counting are efficient and effective.
• Future research can explore the applicability of the shuffle model to other types of graph computations.