Fault-Tolerant Storage and Quorum Systems for Dynamic Environments M.Sc. Thesis

We deal with storage systems and quorum systems for a dynamic environment where servers may join and leave the system. We suggest a file storage system construction based on the ‘And-Or’ quorum system, that has a O( √ n) write complexity, O( √ n log n) read complexity and a constant data blowup-ratio, where n represents the number of processors in the network. Our construction is fault-tolerant against an adversary that can crash θ(n) processors of her choice while having slightly less adaptive queries than the reader. When both the legitimate reader and the adversary are nonadaptive we derive lower bounds on the read complexity, write complexity and data blowup ratio. We show these bounds are tight using a simple storage system construction, based on an 2-intersecting quorum system. In the random-fault model we show that the And-Or quorum system possesses optimal algorithmic probe complexity for both non-adaptive and adaptive readers. The non-adaptive algorithm for finding a live quorum achieves a O( √ n log n) algorithmic probe complexity which matches a lower bound of Naor and Wieder [20]. The adaptive algorithm finds a live quorum with a probe complexity which is linear in the size of a quorum (O( √ n)) and requires at most O(log log n) rounds. To the best of our knowledge, this is the smallest number of rounds in which a live quorum can be found, using only O( √ n) probes, for a system with an optimal load. Last we present an adaptation of the above storage system and a quorum system for a dynamic environment. Both are based on the And-Or tree and a dynamic overlay network that emulates the De-Bruijn network. These adaptations maintain the good properties of the above constructions (e.g., fault-tolerance, load and availability). The algorithms suggested for the maintenance of these dynamic data structures are strongly coupled with the routing scheme of the network. This fact enables the use of gossip protocols which saves in message complexity and keeps the protocols simple and local.