# Distributed Processes and Scalability in Sub-networks of Large-Scale Networks

## TL;DR

This paper introduces distributed iterative processes that focus on subnetwork scopes within large networks, improving scalability for local tasks by controlling subnetwork size with a local parameter.

## Contribution

It presents a novel approach to limit computational scope in distributed processes, with theoretical and experimental analysis of convergence and termination.

## Key findings

- Processes converge faster on smaller subnetworks
- The approach scales better than global methods in large networks
- Theoretical bounds match experimental results

## Abstract

Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$ is the number of nodes. As the size of the network increases, this makes global convergence over the entire network less practical. On the other hand, for several applications, such as load balancing or detection of local events, global convergence may not be necessary or even relevant. We introduce simple distributed iterative processes which limit the scope of the computational task to a smaller subnetwork of the entire network. This is achieved using one additional local parameter which controls the size of the subnetwork. We establish termination and convergence rate of such processes in theory, in experiment, in comparison to the well understood behavior of Markov processes, and for a variety of network topologies and initial conditions.