Algorithms for distributed caching and aggregation
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In recent years, there has been an explosion in the amount of distributed data due to the ever decreasing cost of both storage and bandwidth. There is a growing need for automatic distributed data management techniques. The three main areas in dealing with distributed data that we address in this dissertation are (1) cooperative caching, (2) compression caching, and (3) aggregation. First, we address cooperative caching, in which caches cooperate to locate and cache data objects. The benefits of cooperative caching have been demonstrated by various studies. We address a hierarchical generalization of cooperative caching in which caches are arranged as leaf nodes in a hierarchical tree network, and we call this variant Hierarchical Cooperative Caching. We present a deterministic hierarchical generalization of LRU that is constantcompetitive when the capacity blowup is linear in d, the depth of the cache hierarchy. Furthermore, we show that any randomized hierarchical cooperative caching algorithm with capacity blowup b has competitive ratio Ω(log d b ) against an oblivious adversary. Thus we establish that there is no resource competitive algorithm for the hierarchical cooperative caching problem. Second, we address a class of compression caching problems in which a file can be cached in multiple formats with varying sizes and encode/decode costs. In this work, we address three problems in this class of compression caching. The first problem assumes that the encode cost and decode cost associated with any format of a file are equal. For this problem we present a resource competitive online algorithm. To explore the existence of resource competitive online algorithms for compression caching with arbitrary encode costs and decode costs, we address two other natural problems in the aforementioned class, and for each of these problems, we show that there exists a non-constant lower bound on the competitive ratio of any online algorithm, even if the algorithm is given an arbitrary factor capacity blowup. Thus, we establish that there is no resource competitive algorithm for compression caching in its full generality. Third, we address the problem of aggregation over trees with the goal of adapting aggregation aggressiveness. Consider a distributed network with nodes arranged in a tree, and each node having a local value. We consider the problem of aggregating values (e.g., summing values) from all nodes to the requesting nodes in the presence of writes. The goal is to minimize the total number of messages exchanged. The key challenges are to define a noix tion of “acceptable” aggregate values, and to design algorithms with good performance that are guaranteed to produce such values. We formalize the acceptability of aggregate values in terms of certain consistency guarantees. We propose a lease-based aggregation mechanism, and evaluate algorithms based on this mechanism in terms of consistency and performance. With regard to consistency, we adapt the definitions of strict and causal consistency to apply to the aggregation problem. We show that any lease-based aggregation algorithm provides strict consistency in sequential executions, and causal consistency in concurrent executions. With regard to performance, we propose an online lease-based aggregation algorithm, and show that, for sequential executions, the algorithm is constant competitive against any offline algorithm that provides strict consistency. Our online lease-based aggregation algorithm is presented in the form of a fully distributed protocol, and the aforementioned consistency and performance results are formally established with respect to this protocol. We also present experimental results to show that the algorithm performs well under various workloads.