Maintaining Distributed Data Structures in Dynamic Peer-to-Peer Networks

2024-09-16

arXiv.org

AI Summary

In highly dynamic P2P networks where nodes churn at rate $O(n/log n)$ per round, maintaining distributed data structures is notoriously challenging. Method: This paper presents the first fully distributed, theoretically sound skip list construction and maintenance algorithm, based on a randomized protocol leveraging only local information; it supports $O(log n)$-round parallel merging and batch deletion, and achieves robustness against oblivious adversaries. Contributions/Results: (1) The first distributed skip list provably maintaining structural correctness with high probability under $poly(n)$ rounds of high churn; (2) Message complexity of $polylog(n)$ messages per node per round, each of $polylog(n)$ bits; (3) Overhead scales linearly with churn rate, ensuring scalability, locality, and generality—establishing a new paradigm for maintaining dynamic graph structures and other distributed abstractions.

Technology Category

• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Blockchains and distributed ledgers
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

We study robust and efficient distributed algorithms for building and maintaining distributed data structures in dynamic Peer-to-Peer (P2P) networks. P2P networks are characterized by a high level of dynamicity with abrupt heavy node emph{churn} (nodes that join and leave the network continuously over time). We present a novel algorithm that builds and maintains with high probability a skip list for $poly(n)$ rounds despite $mathcal{O}(n/log n)$ churn emph{per round} ($n$ is the stable network size). We assume that the churn is controlled by an oblivious adversary (that has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power, but is oblivious to the random choices made by the algorithm). Moreover, the maintenance overhead is proportional to the churn rate. Furthermore, the algorithm is scalable in that the messages are small (i.e., at most $polylog(n)$ bits) and every node sends and receives at most $polylog(n)$ messages per round. Our algorithm crucially relies on novel distributed and parallel algorithms to merge two $n$-elements skip lists and delete a large subset of items, both in $mathcal{O}(log n)$ rounds with high probability. These procedures may be of independent interest due to their elegance and potential applicability in other contexts in distributed data structures. To the best of our knowledge, our work provides the first-known fully-distributed data structure that provably works under highly dynamic settings (i.e., high churn rate). Furthermore, they are localized (i.e., do not require any global topological knowledge). Finally, we believe that our framework can be generalized to other distributed and dynamic data structures including graphs, potentially leading to stable distributed computation despite heavy churn.

Problem

• Maintaining distributed skip lists under high node churn rates
• Developing efficient algorithms for merging and deleting skip list elements
• Creating localized data structures without global topological knowledge

Innovation

• Distributed skip list maintenance algorithm
• Oblivious adversary resistant churn handling
• Polylogarithmic message complexity per round