{'fraction_non_alphanumeric': 0.01805372082782915, 'fraction_numerical': 0.006164685160722149, 'mean_word_length': 5.276243093922652, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Supporting multidimensional range queries in Hierarchically Distributed Tree

An examination of the multidimensional range query in existing peer‐to‐peer (P2P) overlay networks indicates that multidimensional range queries are sensitive to underlying topologies; this is because partitioning and mapping of multidimensional data space are two interconnected parts of a process that must be carried out cooperatively. The first section focuses on how to preserve data localities, whereas the second section concerns how to accommodate and maintain data localities at the P2P overlay layer. There are many studies that have been conducted on the first section since 1966, and those works that are well accepted are mostly based on recursive decomposition, which forms a tree structure in nature. However, less effort has been made to provide comparable support from the P2P overlay layer. In our previous work, we proposed the Hierarchically Distributed Tree (HD Tree) in order to better support multidimensional range queries in the P2P overlay network. This paper further explores error‐resilient routing and load balancing strategies that can be employed in the HD Tree. We also provide a complete set of experimental results for all routing operations: Join and Leave of nodes, range queries at different levels of selectivity, and the dynamic load balancing scheme. Comparisons are made by conducting simulations under both the ideal and the error‐prone routing environment and within various ary HD Trees. The experimental results show that load balancing in the HD Tree can be adjusted dynamically and globally, and it is actually a trade‐off between distributing the basic load and the involvement of nodes in range querying. The experimental results also indicate that a maximum of 10 percent of routing nodes’ failures do not have significant effects on the performance of range queries. However, a lower ary HD Tree appears to have better routing performance, whereas a higher ary HD Tree achieves a higher fault‐tolerant capacity. Nevertheless, the performance of range queries in a higher ary HD Tree can be further optimized if all possible routing options can be fully explored in the error‐prone routing environment. Copyright © 2013 John Wiley & Sons, Ltd.