Adaptive Self-Organization in Anonymous Dynamic Networks

2026-04-29

AI Summary

This work addresses the problem of enabling nodes in anonymous, synchronous networks with adversarially dynamic topologies to distributively adjust their color distributions—based solely on locally observed time-varying environmental signals—to converge toward a prescribed target distribution. The study establishes the first characterization of the solvability boundary for this problem, proving that homogeneous target distributions can be exactly achieved in linear time using only logarithmic memory via a deterministic algorithm; moreover, if nodes know the network size, this algorithm exhibits strong convergence robustness against perturbations. By incorporating randomization, the approach is extended to arbitrary target distributions, achieving convergence with high probability. Integrating adversarial dynamic network modeling, deterministic finite-state machine design, and randomized protocol analysis, this work provides both theoretical foundations and efficient algorithms for adaptive self-organization in dynamic anonymous networks.

Abstract

We introduce the problem of adaptive self-organization in which the nodes of an anonymous, synchronous dynamic network must distributively change the collective distribution of their responses (or "colors") as a function of time-varying environmental signals, even when these signals are only perceived locally and the network topology changes adversarially. Specifically, a signal adversary may change the type of signal and which node(s) witness that signal arbitrarily between rounds. If a signal (or lack thereof) $s$ persists in the system for sufficiently long, the dynamic network must stabilize such that nodes' colors reach and remain in a distribution closely approximating $r(s)$, a goal distribution defined by the problem instance. We first prove that if nodes are deterministic, the only solvable instances of adaptive-self organization are those with homogeneous goal distributions, i.e., those where all nodes must stabilize with the same color. We then present a linear-time, logarithmic-memory, deterministic algorithm for this subclass of instances that works even when the multiplicity and location of signal witnesses change arbitrarily. When nodes know $n$, the number of nodes in the network, a small adaptation of this algorithm achieves a stronger convergence property in which adversarial edge and signal dynamics are entirely unable to disturb stabilized configurations. Finally, we present a randomized extension of these algorithms that solves arbitrary (i.e., not necessarily homogeneous) instances of adaptive self-organization with high probability when nodes know the goal distributions.

Problem

• adaptive self-organization
• anonymous dynamic networks
• distributed coloring
• adversarial dynamics
• goal distribution

Innovation

• adaptive self-organization
• anonymous dynamic networks
• deterministic algorithms
• randomized algorithms
• adversarial dynamics