# A Topological Perspective on Distributed Network Algorithms

## TL;DR

This paper applies combinatorial topology to analyze distributed algorithms in failure-free networks, deriving lower bounds for consensus and agreement problems across various network models.

## Contribution

It extends the use of combinatorial topology from fault-tolerant systems to failure-free networks of arbitrary structure, providing new lower bounds.

## Key findings

- Derived lower bounds for consensus and agreement problems.
- Applied topological methods to arbitrary network structures.
- Extended topological analysis to classical distributed models.

## Abstract

More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also be useful for analyzing distributed algorithms in failure-free networks of arbitrary structure. To illustrate this, we analyze consensus, set-agreement, and approximate agreement in networks, and derive lower bounds for these problems under classical computational settings, such as the LOCAL model and dynamic networks.