Differential Privacy Meets Fixed Parameter Tractability: Algorithms and Lower Bounds

2026-09-11

AI Summary

研究在ε-差分隐私约束下，通过允许编码器在固定参数可处理时间内运行来解决组合优化问题，并为该框架设定了首个独立于表示的下界。

Abstract

We study combinatorial optimization problems under the constraint of $ε$-differential privacy ($ε$-DP). Given the strong lower bounds for explicitly outputting solutions, we work within the implicit representation framework of Gupta et al. (SODA 2010), where a private polynomial-time randomized "encoder" generates a representation of a solution, and a "decoder" uses this representation along with the input to extract a valid final solution. In this work, we generalize this framework by allowing the encoder to run in fixed-parameter tractable time. This circumvents approximation barriers inherent to polynomial-time algorithms and obtains improved guarantees for many fundamental combinatorial optimization problems. Finally, we establish the first representation-independent lower bounds for our framework. Assuming a non-uniform variant of the Gap Exponential Time Hypothesis, for sufficiently small $ε> 0$, we prove that no $ε$-DP encoder-decoder pair can achieve certain approximation guarantees, if the decoder runs in subexponential time. We further provide representation-dependent lower bounds that hold even for larger $ε$.

Problem

• Differential Privacy
• Combinatorial Optimization
• Fixed Parameter Tractability
• Approximation Barrier

Innovation

• Differential Privacy
• Fixed Parameter Tractability
• Combinatorial Optimization
• Implicit Representation
• Lower Bounds