# A Tale of Many Networks: Splitting and Merging of Chord-like Overlays in Partitioned Networks
## 1 Introduction  
Structured peer-to-peer (P2P) overlay networks are a class of distributed systems that enable scalable and decentralized data storage and retrieval. In contrast to unstructured overlays, structured overlays organize peers according to a deterministic topology, typically guided by a key-based routing mechanism [1]. In recent decades, different types of overlays emerged. According to the structure of the routing table and the usage of an identifier space, overlays can be categorized into various types like ring-based, tree-based, or mesh-based overlays. In this work, we focus on ring-based overlays, which are characterized by mapping nodes to points of a circular identifier space and by connecting peers according to their position in this identifier space. We choose Chord [2] as an example for this category of overlays, as it is the most cited structured peer-to-peer overlay. It allows detailed investigations on these issues, as solutions may be transferable to other ring-based overlay networks. Ring-based overlays such as Chord [2] or Pastry [3] assign node identifiers in a circular address space and connect nodes based on proximity in this space. This structure enables efficient lookup and robust self-organization, even under churn. One of the core strengths of P2P overlays is their resilience against central points of failure, making them a viable alternative to client-server systems, especially in environments withunreliable or politically controlled infrastructure. Unlike centralized architectures, where content and metadata reside on a few dedicated servers, structured overlays distribute data and responsibilities across all participating peers, making surveillance and censorship significantly more difficult. In contrast to the centralized server architecture, participants in a peer-to-peer network are expected to be unreliable and means for robustness are incorporated in the overlay protocols. User-related information is distributed among peers in a decentralized manner without the need for a dedicated server that could be attacked. The peer-to-peer architecture is, therefore, suitable for sharing data or information dissemination. An example of peer-to-peer-based social networking is LibreSocial [4], an online social network solely hosted by users. It uses the ring-based overlay network Pastry [3] and supports profiles, friend lists, and the storage of images and documents and enables real-time communication. However, this robustness is challenged when large-scale network partitioning occurs, as seen during nationwide Internet shutdowns. Such partitions may fragment the overlay into multiple isolated subnetworks, impeding global consistency, searchability, and data availability. Once connectivity is re-established, these disjoint overlay instances must re-merge efficiently and without user intervention, a non-trivial task for most existing structured overlays. Recent history offers several striking examples of network partitioning:  
* During the Arab Spring in Egypt (2011), from 27 January 2011 until 2 February 2011, approximately 93% of Egyptian networks were unreachable ([[http://www.nytimes.com/2011/01/29/technology/internet/29](http://www.nytimes.com/2011/01/29/technology/internet/29) cutoff.html]([http://www.nytimes.com/2011/01/29/technology/internet/29](http://www.nytimes.com/2011/01/29/technology/internet/29) cutoff.html), accessed on 26 May 2025), and most parts of the Internet in Egypt had been cut off by the Egyptian government ([[http://www.circleid.com/posts/egyptian_government_shuts_down_most_internet_and_cell_services/](http://www.circleid.com/posts/egyptian_government_shuts_down_most_internet_and_cell_services/)]([http://www.circleid.com/posts/egyptian_government_shuts_down_most_internet_and_cell_services/](http://www.circleid.com/posts/egyptian_government_shuts_down_most_internet_and_cell_services/)), accessed on 26 May 2025). * Nepal cut off Internet access entirely in 2005, as did Myanmar two years later in 2007.