HD Tree: A novel data structure to support multi-dimensional range query for P2P networks

There are two basic concerns for supporting multi-dimensional range query in P2P overlay networks. The first is to preserve data locality in the process of data space partitioning, and the second is the maintenance of data locality among data ranges with an exponentially expanding and extending rate. The first problem has been well addressed by using recursive decomposition schemes, such as Quad-tree, K-d tree, ZZ-order, and Hilbert curve. On the other hand, the second problem has been recently identified by our novel data structure: HD Tree. In this paper, we explore how data locality can be easily maintained, and how range query can be efficiently supported in HD Tree. This is done by introducing two basic routing strategies: hierarchical routing and distributed routing. Although hierarchical routing can be applied to any two nodes in the P2P system, it generates high volume traffic toward nodes near the root, and has very limited options to cope with node failure. On the other hand, distributed routing concerns source and destination pairs only at the same depth, but traffic load is bound to some nodes at two neighboring depths, and multiple options can be found to redirect a routing request. Because HD Tree supports multiple routes between any two nodes in the P2P system, routing in HD Tree is very flexible; it can be designed for many purposes, like fault tolerance, or dynamic load balancing. Distributed routing oriented combined routing (DROCR) algorithm is one such routing strategy implemented so far. It is a hybrid algorithm combining advantages from both hierarchical routing and distributed routing. The experimental results show that DROCR algorithm achieves considerable performance gain over the equivalent tree routing at the highest depth examined. For supporting multi-dimensional range query, the experimental results indicate that the exponentially expanding and extending rate have been effectively controlled and minimized by HD Tree overlay structure and DROCR routing.

► Novel data structure built to support MDR at the P2P network layer.
► Additional distributive feature at the cost of doubling total links of tree.
► Direct mapping from data space to identifier space.
► MDR with a complete selectivity in 6D data space has been examined.
► Basic operations are bound by O(lg(n))O(lg(n)).