The Impact of Communication Patterns on Distributed Self-Adjusting Binary Search Tree

This paper introduces the problem of communication pattern adaption for a distributed self-adjusting binary search tree. We propose a simple local algorithm that is closely related to the over thirty-year-old idea of splay trees and evaluate its adaption performance in the distributed scenario if different communication patterns are provided. To do so, the process of self-adjustment is modeled similarly to a basic network creation game in which the nodes want to communicate with only a certain subset of all nodes. We show that, in general, the game (i.e., the process of local adjustments) does not converge, and that convergence is related to certain structures of the communication interests, which we call conflicts. We classify conflicts and show that for two communication scenarios in which convergence is guaranteed, the self-adjusting tree performs well. Furthermore, we investigate the different classes of conflicts separately and show that, for a certain class of conflicts, the performance of the tree network is asymptotically as good as the performance for converging instances. However, for the other conflict classes, a distributed self-adjusting binary search tree adapts poorly.