Wormhole: A Fast Ordered Index for In-memory Data Management (1805.02200v2)

Abstract: In-memory data management systems, such as key-value stores, have become an essential infrastructure in today's big-data processing and cloud computing. They rely on efficient index structures to access data. While unordered indexes, such as hash tables, can perform point search with O(1) time, they cannot be used in many scenarios where range queries must be supported. Many ordered indexes, such as B+ tree and skip list, have a O(log N) lookup cost, where N is number of keys in an index. For an ordered index hosting billions of keys, it may take more than 30 key-comparisons in a lookup, which is an order of magnitude more expensive than that on a hash table. With availability of large memory and fast network in today's data centers, this O(log N) time is taking a heavy toll on applications that rely on ordered indexes. In this paper we introduce a new ordered index structure, named Wormhole, that takes O(log L) worst-case time for looking up a key with a length of L. The low cost is achieved by simultaneously leveraging strengths of three indexing structures, namely hash table, prefix tree, and B+ tree, to orchestrate a single fast ordered index. Wormhole's range operations can be performed by a linear scan of a list after an initial lookup. This improvement of access efficiency does not come at a price of compromised space efficiency. Instead, Wormhole's index space is comparable to those of B+ tree and skip list. Experiment results show that Wormhole outperforms skip list, B+ tree, ART, and Masstree by up to 8.4x, 4.9x, 4.3x, and 6.6x in terms of key lookup throughput, respectively.

• The paper introduces Wormhole, which reduces lookup complexity to O(logL) and significantly outperforms traditional indices.
• It combines hash tables, prefix tries, and B+ trees to efficiently handle both point and range queries in memory.
• Experimental results demonstrate Wormhole’s throughput gains, outperforming skip lists, B+ trees, ART, and Masstree by up to 8.4x.

An Analysis of "Wormhole: A Fast Ordered Index for In-memory Data Management"

The paper "Wormhole: A Fast Ordered Index for In-memory Data Management" introduces an optimized data structure aimed at addressing the inefficiencies inherent in traditional ordered indices. With the surge in in-memory data management systems for key-value storage supporting complex data processing tasks, there's a need for highly efficient indexing structures that are not only fast but also support a variety of operations, including range queries and point lookups. The traditional structures like B+ trees and skip lists falter in these scenarios due to their O(logN) lookup time, which becomes prohibitive with the large scale of data handled in modern applications. The Wormhole index offers a promising alternative by achieving a lookup cost of O(logL), with L being the length of the search key, hence optimizing performance for workloads with varying key lengths.

Key Innovations and Numerical Results

Wormhole is constructed by intricately blending three indexing structures: hash tables, prefix tries, and B+ trees. The ingenious orchestration of these enables the resolution of key lookups by efficiently directing search paths and minimizing search time. The Wormhole structure applies a combined approach utilizing the hash table's O(1) access time, the prefix tree's space efficiency, and the B+ tree's organization for storing multiple items in a node.

Experimentally, Wormhole demonstrated superiority over traditional structures. Performance metrics revealed Wormhole outpaced skip lists by 8.4 times, B+ trees by 4.9 times, ART by 4.3 times, and Masstree by 6.6 times concerning key lookup throughput. This extensive benchmark testing establishes Wormhole not only as a faster index for point queries but also as a viable candidate for applications that require efficient range queries.

Theoretical and Practical Implications

From a theoretical perspective, the introduction of a combined data structure leveraging the strengths of multiple traditional structures brings forward a significant improvement in the asymptotic complexity of ordered indices operations. This innovation has potential implications for the design considerations in data structures where key length variation and volume significantly affect performance.

Practically, adopting Wormhole can result in substantial computational savings and enhanced throughput in big data applications and cloud-based infrastructures where in-memory data management is prevalent. The reduced lookup time fosters efficiency, especially in scenarios where rapid data access is critical, elevating system performance close to hardware limits.

Speculations and Future Directions

Considering ongoing developments in AI and large-scale data processing, the Wormhole index’s design might inspire future adaptations or improvements. The optimization of anchoring strategies, concurrency control mechanisms, and further enhancements in reducing memory footprint could become focal points of future research. Another promising area for exploration is adapting the Wormhole design to novel hardware environments, such as those incorporating non-volatile memory technologies, which could further exploit its efficiency for persistent data management tasks.

In conclusion, the Wormhole index represents a significant stride forward in ordered indexing for in-memory data management systems. Its introduction addresses the prevalent need for efficient data structures that can handle the dual requirements of speed and capability. By efficiently bridging the performance gap between unordered and ordered indices, Wormhole reflects a well-conceived innovation balancing theoretical soundness and practical applicability.