BMMI-tree: A Peer-to-Peer m-ary tree using 1-m node splitting for an efficient multidimensional complex query search

Abstract

Peer-to-Peer (P2P) applications such as content distribution and sharing (like file, audio, video), multiuser communication (games, desktop sharing, e-learning) have emerged as a new paradigm over a last decade. However, scalability requirements remain a major concern and hence, the distribution and effective search of multidimensional data have become major challenges for P2P computing. Most of the existing P2P overlays either do not give support to Multidimensional Indexing (MI) or the frameworks are less efficient for complex query search or they are limited up to binary trees only, with the search complexity O(log2N). However, traditional MI based on m-ary tree is strengthened for the complex query search (bound to logmN) using higher fanout, m> 2. Based on these observations, we propose BMMI-tree (Balanced Multiway Multidimensional Indexing-tree) that uses an m-ary P2P tree overlay network and also provides the support of MI tree indexing methods such as R-tree or SS-tree in this paper. The paper also analyzes the complex query search algorithms performed in O(logmN) steps with the experimental results. In addition, the construction of the P2P tree network requires to split some existing node and its data objects into m new child nodes (during node join) and vice versa (during node leave). To the best of our knowledge, none of the existing node splitting algorithms for multiway multidimensional trees offer 1-m node splitting. Hence, in this paper, we also propose two different approaches to split the MI tree node into m number of nodes (m-ary split) to be used effectively to create a dynamic tree overlay. Lastly, we present how the BMMI-tree can be applied for service provisioning in cloud computing in a decentralized and distributed manner.