Efficient and accurate protocols for distributed delaunay triangulation under churn

Abstract

We design a new suite of protocols for a set of nodes in d-dimension (d > 1) to construct and maintain a distributed Delaunay triangulation (DT) in a dynamic environment. The join, leave, and failure protocols in the suite are proved to be correct for a single join, leave, and failure, respectively. For a system under churn, it is impossible to maintain a correct distributed DT continually. We define an accuracy metric such that accuracy is 100% if and only if the distributed DT is correct. The suite also includes a maintenance protocol designed to recover from incorrect system states and to improve accuracy. In designing the protocols, we make use of two novel observations to substantially improve protocol efficiency. First, in the neighbor discovery process of a node, many replies to the nodepsilas queries contain redundant information. Second, the use of a new failure protocol that employs a proactive approach to recovery is better than the reactive approaches used in prior work. Experimental results show that our new suite of protocols maintains high accuracy for systems under churn and each system converges to 100% accuracy after churning stopped. They are much more efficient than protocols in prior work.