Epidemic algorithms for replicated database maintenance
PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
ACM Transactions on Computer Systems (TOCS)
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Efficient Routing in Networks with Long Range Contacts
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Lightweight probabilistic broadcast
ACM Transactions on Computer Systems (TOCS)
Eclecticism shrinks even small worlds
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
The peer sampling service: experimental evaluation of unstructured gossip-based implementations
Proceedings of the 5th ACM/IFIP/USENIX international conference on Middleware
Euro-Par'05 Proceedings of the 11th international Euro-Par conference on Parallel Processing
Know thy neighbor’s neighbor: better routing for skip-graphs and small worlds
IPTPS'04 Proceedings of the Third international conference on Peer-to-Peer Systems
Modularity: a first class concept to address distributed systems
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T-Man: Gossip-based fast overlay topology construction
Computer Networks: The International Journal of Computer and Telecommunications Networking
Adaptive Peer Sampling with Newscast
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Peer to peer multidimensional overlays: approximating complex structures
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Biased selection for building small-world networks
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
A case for random shortcut topologies for HPC interconnects
Proceedings of the 39th Annual International Symposium on Computer Architecture
Brief announcement: node sampling using centrifugal random walks
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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In small-world networks, each peer is connected to its closest neighbors in the network topology, as well as to additional long-range contact(s), also called shortcut(s). In 2000, Kleinberg provided asymptotic lower bounds on routing performances and showed that greedy routing in an n-peer small-world network performs in Ω(n1/3) steps when the distance to shortcuts is chosen uniformly at random, and in Θ(log2 n) when the distance to shortcuts is chosen according to a harmonic distribution in a d-dimensional mesh. Yet, we observe through experimental results that peer to peer gossip-based protocols achieving small-world topologies where shortcuts are randomly chosen, perform reasonably well in practice. Kleinberg results are relevant for extremely large systems while systems considered in practice are usually of smaller size (they are typically made up of less than one million of peers). This paper explores the impact of Kleinberg results in the context of practical systems and small-world networks. More precisely, based on the observation that, despite the fact that the routing complexity of gossipbased small-world overlay networks is not polylogarithmic (as proved by Kleinberg), this type of networks ultimately provide reasonable results in practice. This leads us to think that the asymptotic big O() complexity alone might not always be sufficient to assess the practicality of a system whose size is typically smaller that what the one theory targets. The paper consequently proposes a refined routing complexity measure for small-world networks (namely, a recurrence formula that can be easily computed). Yet, given that Kleinberg proved that the distribution of shortcuts has a strong impact on the routing complexity (when extremely large networks are considered), arises the question of leveraging this result to improve upon current gossip-based protocols. We show that gossip-based protocols (designed for less than one million of peers) can benefit from a good approximation of Kleinberg-like small-world topologies (designed for extremely large networks). Along, are presented simulation results that demonstrate the relevance of the proposed approach.