SeedTree: A Dynamically Optimal and Local Self-Adjusting Tree

TL;DR

SeedTree is a new self-adjusting tree data structure that dynamically optimizes itself for demand, supporting local routing and demonstrating both theoretical optimality and practical efficiency on real-world data.

Contribution

We introduce SeedTree, a self-adjusting tree that is dynamically optimal, supports local routing, and is designed for highly dynamic demands, with both theoretical and empirical validation.

Findings

SeedTree achieves dynamic optimality in self-adjusting trees.

It supports local greedy routing efficiently.

Empirical tests show improved performance on real-world traces.

Abstract

We consider the fundamental problem of designing a self-adjusting tree, which efficiently and locally adapts itself towards the demand it serves (namely accesses to the items stored by the tree nodes), striking a balance between the benefits of such adjustments (enabling faster access) and their costs (reconfigurations). This problem finds applications, among others, in the context of emerging demand-aware and reconfigurable datacenter networks and features connections to self-adjusting data structures. Our main contribution is SeedTree, a dynamically optimal self-adjusting tree which supports local (i.e., greedy) routing, which is particularly attractive under highly dynamic demands. SeedTree relies on an innovative approach which defines a set of unique paths based on randomized item addresses, and uses a small constant number of items per node. We complement our analytical results by showing the benefits of SeedTree empirically, evaluating it on various synthetic and real-world communication traces.