# Distributed Monitoring of Topological Events via Homology

## TL;DR

This paper presents a distributed method for detecting topological events in sensor networks by leveraging local graph changes and homology, enabling accurate detection of multiple concurrent events.

## Contribution

It introduces a novel model that uses graph homology and Betti number differences to detect and categorize topological events in dynamic sensor networks.

## Key findings

- Effective detection of non-incremental topological events
- Region updates are conflict-free and order-independent
- Method accurately categorizes multiple concurrent events

## Abstract

Topological event detection allows for the distributed computation of homology by focusing on local changes occurring in a network over time. In this paper, a model for the monitoring of topological events in dynamically changing regions will be developed. Regions are approximated as the connected components of the communication graph of a sensor network, reducing homology computation to graph homology. Betti number differences together with cyclic neighbor-rings are used to categorize topological event types. The focus lies on the correct detection of non-incremental (i.e., multiple concurrently occurring) events and the necessary region update process. Network number differences between a network's state before and after events are spread from event nodes into network regions, allowing for the conflict-free updating of regions independent of the update messages' order of arrival.