Scalable and dynamic quorum systems

Moni Naor, Udi Wieder
2005 Distributed computing  
We investigate issues related to the probe complexity of quorum systems and their implementation in a dynamic environment. Our contribution is twofold. The first regards the algorithmic complexity of finding a quorum in case of random failures. We show a tradeoff between the load of a quorum system and its probe complexity for non adaptive algorithms. We analyze the algorithmic probe complexity of the Paths quorum system suggested by Naor and Wool in [28] , and present two optimal algorithms.
more » ... e first is a non adaptive algorithm that matches our lower bound. The second is an adaptive algorithm with a probe complexity that is linear in the cardinality of the smallest quorum set. We supply a constant degree network in which these algorithms could be executed efficiently. Thus the Paths quorum system is shown to have good balance between many measures of quality. Our second contribution is presenting Dynamic Paths -a suggestion for a dynamic and scalable quorum system, which can operate in an environment where elements join and leave the system. The quorum system could be viewed as a dynamic adaptation of the Paths system, and therefore has low load high availability and good probe complexity. We show that it scales gracefully as the number of elements grows. 1. It is often assumed that processors can somehow find and communicate with one another. We analyze algorithms for finding quorum systems in a distributed network while taking into account the network implementation; i.e., the network and the quorum system should be compatible such that elements from the same quorum are connected to one another. We supply algorithms for finding a quorum set (even in the case of failures) and analyze their running time and communication complexity. In this setting non-adaptive algorithms are attractive since they can be executed in parallel. 2. The setting in which the quorum operates is often dynamic, and should accommodate changes in the quorum system over time. See for instance [21] , [33] . We address the problem of designing a quorum system that is fit for a scalable and dynamic environment where processors leave and join at will. Abraham and Malkhi [3] address this problems when the intersection property is not guaranteed but rather occurs with high probability. Scalable Dynamic Data Structures -P2P Recently a new approach for construction of dynamic distributed data structures on overlay networks was suggested, which offers excellent scalability. The main motivation for this line of research comes from the rise in popularity of P2P application, therefore the attention was put on the construction of distributed hash tables (cf. [26], [23] , [34], [32]). In these works an overlay network is built dynamically. Processors may fail (with some probability) and are allowed to join and leave. Each processor holds some data items. The construction in [26] for instance, guarantees that any data item could be found in logarithmic time, while imposing small load on every processor. In this paper we suggest quorum systems that operate in a dynamic peer-to-peer model. We combine techniques developed in these papers, mainly [26] and [32], with appropriate quorum systems, and provide the distributed algorithms for finding the quorums. We allow two types of events:
doi:10.1007/s00446-004-0114-3 fatcat:xm3bmtyozreh3o6zkmd3akvcua