Online Aggregation over Trees

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 notion 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.