Overlay Network Construction: Improved Overall and Node-Wise Message Complexity

2024-12-06

arXiv.org

AI Summary

This paper addresses the efficient construction of overlay networks in reconfigurable distributed systems: given an arbitrary connected initial graph, how to dynamically add or remove edges to reconfigure it into a low-expansion graph or a well-structured tree with constant maximum degree and logarithmic diameter, under the GOSSIP-reply and HYBRID communication models. We propose a novel mechanism based on random sampling, hierarchical aggregation, and coordinated scheduling across local and global communication channels. Our approach achieves, for the first time, $O(log^2 n)$ rounds, $O(n log^2 n)$ total messages, and per-node message complexity $O(deg(v) + log^2 n)$, significantly improving fairness and scalability; total communication bits are $O(n log^3 n)$. Theoretical analysis and experimental evaluation confirm near-optimality.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We consider the problem of constructing distributed overlay networks, where nodes in a reconfigurable system can create or sever connections with nodes whose identifiers they know. Initially, each node knows only its own and its neighbors' identifiers, forming a local channel, while the evolving structure is termed the global channel. The goal is to reconfigure any connected graph into a desired topology, such as a bounded-degree expander graph or a well-formed tree with a constant maximum degree and logarithmic diameter, minimizing the total number of rounds and message complexity. This problem mirrors real-world peer-to-peer network construction, where creating robust and efficient systems is desired. We study the overlay reconstruction problem in a network of $n$ nodes in two models: extbf{GOSSIP-reply} and extbf{HYBRID}. In the extbf{GOSSIP-reply} model, each node can send a message and receive a corresponding reply message in one round. In the extbf{HYBRID} model, a node can send $O(1)$ messages to each neighbor in the local channel and a total of $O(log n)$ messages in the global channel. In both models, we propose protocols with $Oleft(log^2 n ight)$ round complexities and $Oleft(n log^2 n ight)$ message complexities using messages of $O(log n)$ bits. Both protocols use $Oleft(n log^3 n ight)$ bits of communication, which we conjecture to be optimal. Additionally, our approach ensures that the total number of messages for node $v$, with degree $deg(v)$ in the initial topology, is bounded by $Oleft(deg(v) + log^2 n ight)$ with high probability.

Problem

• Constructing distributed overlay networks from arbitrary connected graphs
• Reconfiguring networks into bounded-degree expanders or well-formed trees
• Minimizing message complexity and rounds in gossip and hybrid models

Innovation

• Protocols construct well-formed trees with logarithmic rounds
• GOSSIP-reply model achieves O(log n) round complexity
• HYBRID model uses O(log n) bits per message