Time- and Communication-Efficient Overlay Network Construction via Gossip

Dufoulon, Fabien; Moorman, Michael; Moses Jr., William K.; Pandurangan, Gopal

Abstract

We focus on the well-studied problem of distributed overlay network construction. We consider a synchronous gossip-based communication model where in each round a node can send a message of small size to another node whose identifier it knows. The network is assumed to be reconfigurable, i.e., a node can add new connections (edges) to other nodes whose identifier it knows or drop existing connections. Each node initially has only knowledge of its own identifier and the identifiers of its neighbors. The overlay construction problem is, given an arbitrary (connected) graph, to reconfigure it to obtain a bounded-degree expander graph as efficiently as possible. The overlay construction problem is relevant to building real-world peer-to-peer network topologies that have desirable properties such as low diameter, high conductance, robustness to adversarial deletions, etc. Our main result is that we show that starting from any arbitrary (connected) graph G on n nodes and m edges, we can construct an overlay network that is a constant-degree expander in polylog rounds using only Õ(n) messages. Our time and message bounds are both essentially optimal (up to polylogarithmic factors). Our distributed overlay construction protocol is very lightweight as it uses gossip (each node communicates with only one neighbor in each round) and also scalable as it uses only Õ(n) messages, which is sublinear in m (even when m is moderately dense). To the best of our knowledge, this is the first result that achieves overlay network construction in polylog rounds and o(m) messages. Our protocol uses graph sketches in a novel way to construct an expander overlay that is both time and communication efficient. A consequence of our overlay construction protocol is that distributed computation can be performed very efficiently in this model. In particular, a wide range of fundamental tasks such as broadcast, leader election, and minimum spanning tree (MST) construction can be accomplished in polylog rounds and Õ(n) message complexity in any graph.

Citation

Dufoulon, F., Moorman, M., Moses Jr., W. K., & Pandurangan, G. (2024, January). Time- and Communication-Efficient Overlay Network Construction via Gossip. Presented at ITCS 2024: Innovations in Theoretical Computer Science (ITCS), Berkeley, California

• Presentation Conference Type: Conference Paper (published)
• Conference Name: ITCS 2024: Innovations in Theoretical Computer Science (ITCS)
• Start Date: Jan 30, 2024
• End Date: Feb 2, 2024
• Acceptance Date: Nov 8, 2023
• Online Publication Date: Jan 24, 2024
• Publication Date: 2024
• Deposit Date: Dec 8, 2023
• Publicly Available Date: Jan 24, 2024
• Publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
• Peer Reviewed: Peer Reviewed
• Volume: 287
• Pages: 42:1-42:23
• Series Title: Leibniz International Proceedings in Informatics (LIPIcs)
• Book Title: 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)
• ISBN: 9783959773096
• DOI: https://doi.org/10.4230/LIPIcs.ITCS.2024.42
• Public URL: https://durham-repository.worktribe.com/output/1985124