Maintaining Random Assignments under Adversarial Dynamics

2026-04-07

AI Summary

This work addresses the vulnerability of existing randomized allocation schemes in adversarial dynamic environments, where adaptive adversaries can exploit “timing attacks” to introduce bias. To counter this, the authors propose a “temporal aggregation” principle and design two novel resampling mechanisms that effectively eliminate such bias while updating only a small number of elements per step. By integrating active resampling with a graph algorithmic framework, the approach achieves $O(\Delta)$-coloring for general graphs and $O(\Delta/\log\Delta)$-coloring for triangle-free graphs. The method maintains the distribution of random walks on dynamic graphs with an average update cost sublinear in the number of vertices, ensuring both theoretical guarantees and practical efficiency.

Abstract

We study and further develop powerful general-purpose schemes to maintain random assignments under adversarial dynamic changes. The goal is to maintain assignments that are (approximately) distributed similarly as a completely fresh resampling of all assignments after each change, while doing only a few resamples per change. This becomes particularly interesting and challenging when dynamics are controlled by an adaptive adversary. Our work builds on and further develops the proactive resampling technique [Bhattacharya, Saranurak, and Sukprasert ESA'22]. We identify a new ``temporal selection'' attack that adaptive adversaries can use to cause biases, even against proactive resampling. We propose a new ''temporal aggregation'' principle that algorithms should follow to counteract these biases, and present two powerful new resampling schemes based on this principle. We give various applications of our new methods. The main one in maintaining proper coloring of the graph under adaptive adversarial modifications: we maintain $O(Δ)$ coloring for general graphs with maximum degree $Δ$ and $O(\fracΔ{\ln Δ})$ coloring for triangle free graphs, both with sublinear in the number of vertices average work per modification. Other applications include efficiently maintaining random walks in dynamically changing graphs.

Problem

• random assignments
• adversarial dynamics
• adaptive adversary
• dynamic graphs
• resampling

Innovation

• proactive resampling
• temporal aggregation
• adaptive adversary
• dynamic graph coloring
• random assignment