Query rewriting is often a prerequisite for effective query optimization, particularly for poorly-written queries. Prior work on query rewriting has relied on a set of "rules" based on syntactic pattern-matching. Whether relying on manual rules or auto-generated ones, rule-based query rewriters are inherently limited in their ability to handle new query patterns. Their success is limited by the quality and quantity of the rules provided to them. To our knowledge, we present the first synthesis-based query rewriting technique, SlabCity, capable of whole-query optimization without relying on any rewrite rules. SlabCity directly searches the space of SQL queries using a novel query synthesis algorithm that leverages a new concept called query dataflows. We evaluate SlabCity on four workloads, including a newly curated benchmark with more than 1000 real-life queries. We show that not only can SlabCity optimize more queries than state-of-the-art query rewriting techniques, but interestingly, it also leads to queries that are significantly faster than those generated by rule-based systems.

The inner-product navigable small world graph (ip-NSW) represents the state-of-the-art method for approximate maximum inner product search (MIPS) and it can achieve an order of magnitude speedup over the fastest baseline. However, to date it is still unclear where its exceptional performance comes from. In this paper, we show that there is a strong norm bias in the MIPS problem, which means that the large norm items are very likely to become the result of MIPS. Then we explain the good performance of ip-NSW as matching the norm bias of the MIPS problem — large norm items have big in-degrees in the ip-NSW proximity graph and a walk on the graph spends the majority of computation on these items, thus effectively avoids unnecessary computation on small norm items. Furthermore, we propose the ip-NSW+ algorithm, which improves ip-NSW by introducing an additional angular proximity graph. Search is first conducted on the angular graph to find the angular neighbors of a query and then the MIPS neighbors of these angular neighbors are used to initialize the candidate pool for search on the inner-product proximity graph. Experiment results show that ip-NSW+ consistently and significantly outperforms ip-NSW and provides more robust performance under different data distributions.

As an effective solution to the approximate nearest neighbors (ANN) search problem, learning to hash (L2H) is able to learn similarity-preserving hash functions tailored for a given dataset. However, existing L2H research mainly focuses on improving query performance by learning good hash functions, while Hamming ranking (HR) is used as the default querying method. We show by analysis and experiments that Hamming distance, the similarity indicator used in HR, is too coarse-grained and thus limits the performance of query processing. We propose a new fine-grained similarity indicator, quantization distance (QD), which provides more information about the similarity between a query and the items in a bucket. We then develop two efficient querying methods based on QD, which achieve significantly better query performance than HR. Our methods are general and can work with various L2H algorithms. Our experiments demonstrate that a simple and elegant querying method can produce performance gain equivalent to advanced and complicated learning algorithms.