Abstract
In Peer-to-Peer networks based on consistent hashing and ring topology, each server is responsible for an interval chosen (pseudo-) randomly on a unit circle. The topology of the network, the communication load, and the amount of data a server stores depend heavily on the length of its interval.
Additionally, the nodes are allowed to join the network or to leave it at any time. Such operations can destroy the balance of the network, even if all the intervals had equal lengths in the beginning.
This paper deals with the task of keeping such a system balanced, so that the lengths of intervals assigned to the nodes differ at most by a constant factor. We propose a simple fully distributed scheme, which works in a constant number of rounds and achieves optimal balance with high probability. Each round takes time at most \(\mathcal{O}(\mathcal{D}+{\rm log n})\), where \(\mathcal{D}\) is the diameter of a specific network (e.g. Θ(log n) for Chord [15] and \(\Theta(\frac{log n}{log log n})\) for the continous-discrete approach proposed by Naor and Wieder [12,11]).
The scheme is a continuous process which does not have to be informed about the possible imbalance or the current size of the network to start working. The total number of migrations is within a constant factor from the number of migrations generated by the optimal centralized algorithm starting with the same initial network state.
Partially supported by DFG-Sonderforschungsbereich 376 “Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen” and by the Future and Emerging Technologies programme of EU under EU Contract 001907 DELIS ”Dynamically Evolving, Large Scale Information Systems”.
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Bienkowski, M., Korzeniowski, M., der Heide, F.M.a. (2005). Dynamic Load Balancing in Distributed Hash Tables. In: Castro, M., van Renesse, R. (eds) Peer-to-Peer Systems IV. IPTPS 2005. Lecture Notes in Computer Science, vol 3640. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558989_20
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DOI: https://doi.org/10.1007/11558989_20
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