Hierarchically distributed tree

The Hierarchically Distributed Tree (HD Tree) is a novel distributed data structure. The purpose of proposing this new data structure is for better maintaining data localities with exponentially expanding and extending rate, and at the same time adapting the hierarchical structure to the distributed environment. In HD Tree, the routing table size is determined by the system parameter k, the performance of all basic operations are bound by O(lg(n)). The add-on distributed structure in HD Tree generates multiple routes between any two nodes in the system, and the progressive routing in HD Tree can be conducted more strategically because of the global awareness about the location of each node. Operations in HD Tree can be designed highly error resilient, and the hierarchical nature in HD Tree makes load balancing straightforward, and it is massively scalable not only in multidimensional rang queries, but also in constructing and maintaining P2P overlay structures.