Approximate membership query (AMQ) data structures can approximately determine whether an element is in the set with high efficiency. They are widely used in distributed systems, database systems, bioinformatics, IoT applications, data stream mining, etc. However, the memory consumption of AMQ data structures grows rapidly as the data scale grows, which limits the system's ability to process a massive amount of data. The emerging persistent memory provides a close-to-DRAM access speed and terabyte-level capacity, facilitating AMQ data structures to handle massive data. Nevertheless, existing AMQ data structures perform poorly on persistent memory due to intensive random accesses and/or sequential writes. Therefore, we propose a novel AMQ data structure called wormhole filter, which achieves high performance on persistent memory by reducing random accesses and sequential writes. In addition, we reduce the number of log records for lower recovery overhead. Theoretical analysis and experimental results show that wormhole filters significantly outperform competitive state-of-the-art AMQ data structures. For example, wormhole filters achieve 23.26× insertion throughput, 1.98× positive lookup throughput, and 8.82× deletion throughput of the best competing baseline.

Index structures are powerful tools for improving query performance and reducing disk access in database systems. Multi-dimensional indexes, in particular, are used to filter records effectively based on multiple attributes. Classical multi-dimensional index structures, such as KD-Tree, Quadtree, and R-Tree, have been widely used in modern databases. However, advancements in hardware and algorithms have led to the emergence of new types of multi-dimensional index structures. In this paper, we begin by reviewing classical multi-dimensional indexes. Next, we explore the approaches that leverage modern hardware features, such as Solid-State Drive, Non-Volatile Memory, Dynamic Random Access Memory, and Graphics Processing Unit, to improve the performance of multi-dimensional indexes in various aspects. Then, we investigate the novel work of multi-dimensional indexes that apply state-of-the-art machine learning techniques. Finally, we discuss the challenges and future research directions for multi-dimensional indexing methods.

The approximate membership query (AMQ) data structure is a kind of space-efficient probabilistic data structure. It can approximately indicate whether an element exists in a set. The AMQ data structure has been widely used in network measurements, network security, network caching,etc. Resizing is an extensively utilized operation of the AMQ data structure, but it can lead to system performance degradation. We summarize two main problems that lead to such degradation. Specifically, one of them is that the resizing operation can block other operations, while the other one is that the throughput of AMQ structures will deteriorate after multiple resizing operations due to more computation cost. However, existing related work cannot alleviate both of them. Therefore, we propose a novel AMQ data structure called bamboo filters, which can alleviate the two problems simultaneously. Bamboo filters can insert, look up, and delete an element in constant time. They can also dynamically resize in a fine-grained way. Furthermore, we propose space utilization adaptive bamboo filters that adaptively trigger resizing operations according to the space utilization, thereby achieving lower average memory consumption. Experimental results show that our scheme significantly outperforms state-of-the-art work. Especially, bamboo filters achieve 2.12$\times$lookup throughput of the logarithmic dynamic cuckoo filter.