D3-Tree: A Dynamic Distributed Deterministic Load - Balancer for decentralized tree structures

In this work, we propose D-Tree, a dynamic distributed deterministic structure for data management in decentralized networks. We present in brief the theoretical algorithmic analysis, in which our proposed structure is based on, and we describe thoroughly the key aspects of the implementation. Conducting experiments, we verify that the implemented structure outperforms other well-known hierarchical tree-based structures, since it provides better complexities regarding load-balancing operations. More specifically, the structure achieves an O(logN) amortized bound (N is the number of nodes present in the network), using an efficient deterministic load-balancing mechanism, which is general enough to be applied to other hierarchical tree-based structures. Moreover, we investigate the structure’s fault tolerance, which hasn’t been sufficiently tackled in previous work, both theoretically and through rigorous experimentation. We prove that D-Tree is highly fault tolerant, since, even for massive node failures, it achieves a significant success rate in element queries. Afterwards we go one step further, in order to achieve sub-logarithmic complexity and propose the ART structure (Autonomous Range Tree), exploiting the excellent performance of D-Tree. ART achieves an O(log2b logN) communication cost for query and update operations (b is a double-exponentially power of 2 and N is the total number of peers). Moreover, ART is a fully dynamic and fault-tolerant structure, which supports the join/leave node operations in O(log logN) expected w.h.p number of hops and performs load-balancing in O(log logN) amortized cost.