DeepAI AI Chat
Log In Sign Up

Robust Comparison in Population Protocols

by   Dan Alistarh, et al.

There has recently been a surge of interest in the computational and complexity properties of the population model, which assumes n anonymous, computationally-bounded nodes, interacting at random, and attempting to jointly compute global predicates. In particular, a significant amount of work, has gone towards investigating majority and consensus dynamics in this model: assuming that each node is initially in one of two states X or Y, determine which state had higher initial count. In this paper, we consider a natural generalization of majority/consensus, which we call comparison. We are given two baseline states, X_0 and Y_0, present in any initial configuration in fixed, possibly small counts. Importantly, one of these states has higher count than the other: we will assume |X_0| > C |Y_0| for some constant C. The challenge is to design a protocol which can quickly and reliably decide on which of the baseline states X_0 and Y_0 has higher initial count. We propose a simple algorithm solving comparison: the baseline algorithm uses O(log n) states per node, and converges in O(log n) (parallel) time, with high probability, to a state where whole population votes on opinions X or Y at rates proportional to initial |X_0| vs. |Y_0| concentrations. We then describe how such output can be then used to solve comparison. The algorithm is self-stabilizing, in the sense that it converges to the correct decision even if the relative counts of baseline states X_0 and Y_0 change dynamically during the execution, and leak-robust, in the sense that it can withstand spurious faulty reactions. Our analysis relies on a new martingale concentration result which relates the evolution of a population protocol to its expected (steady-state) analysis, which should be broadly applicable in the context of population protocols and opinion dynamics.


page 1

page 2

page 3

page 4


A stable majority population protocol using logarithmic time and states

We study population protocols, a model of distributed computing appropri...

Fast Convergence of k-Opinion Undecided State Dynamics in the Population Protocol Model

We analyze the convergence of the k-opinion Undecided State Dynamics (US...

An O(log^3/2n) Parallel Time Population Protocol for Majority with O(log n) States

In population protocols, the underlying distributed network consists of ...

Byzantine-Resilient Population Protocols

Population protocols model information spreading in networks where pairw...

On the Metastability of Quadratic Majority Dynamics on Clustered Graphs and its Biological Implications

We investigate the behavior of a simple majority dynamics on network top...

Self-Stabilizing Phase Clocks and the Adaptive Majority Problem

We present a self-stabilising phase clock for population protocols. In t...

Distributed Computation with Continual Population Growth

Computing with synthetically modified bacteria is a vibrant and active f...