# On Counting the Population Size

We consider the problem of counting the population size in the population model. In this model, we are given a distributed system of n identical agents which interact in pairs with the goal to solve a common task. In each time step, the two interacting agents are selected uniformly at random. In this paper, we consider so-called uniform protocols, where the actions of two agents upon an interaction may not depend on the population size n. We present two population protocols to count the size of the population: protocol Approximate, which computes with high probability either n or n, and protocol CountExact, which computes the exact population size in optimal O(nn) interactions, using Õ(n) states. Both protocols can also be converted to stable protocols that give a correct result with probability 1 by using an additional multiplicative factor of O(n) states.

## Authors

• 8 publications
• 12 publications
• 5 publications
05/13/2018

### Exact size counting in uniform population protocols in nearly logarithmic time

We study population protocols: networks of anonymous agents that interac...
03/20/2020

### Message complexity of population protocols

The standard population protocol model assumes that when two agents inte...
05/07/2020

### Simulating Population Protocols in Sub-Constant Time per Interaction

We consider the problem of efficiently simulating population protocols. ...
03/07/2017

### Vocabulary Alignment in Openly Specified Interactions

The problem of achieving common understanding between agents that use di...
06/18/2018

### Fractal Scaling of Population Counts Over Time Spans

Attributes which are infrequently expressed in a population can require ...
05/12/2021

### A survey of size counting in population protocols

The population protocol model describes a network of n anonymous agents ...
03/07/2018

### Population stability: regulating size in the presence of an adversary

We introduce a new coordination problem in distributed computing that we...
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