Lightning Fast and Space Efficient Inequality Joins

Inequality joins, which join relational tables on inequality conditions, are used in various applications. While there have been a wide range of optimization methods for joins in database systems, from algorithms such as sort-merge join and band join, to various indices such as B-tree, R⇤-tree and Bitmap, inequality joins have received little attention and queries containing such joins are usually very slow. In this paper, we introduce fast inequality join algorithms. We put columns to be joined in sorted arrays and we use permutation arrays to encode positions of tuples in one sorted array w.r.t. the other sorted array. In contrast to sort-merge join, we use space e cient bit-arrays that enable optimizations, such as Bloom filter indices, for fast computation of the join results. We have implemented a centralized version of these algorithms on top of PostgreSQL, and a distributed version on top of Spark SQL. We have compared against well known optimization techniques for inequality joins and show that our solution is more scalable and several orders of magnitude faster. 1. ONCE UPON A TIME . . . Bob, a data analyst working for an international provider of cloud services, wanted to analyze revenue and utilization trends from di↵erent regions. In particular, he wanted to find out all those transactions from the West-Coast that last longer and produce smaller revenues than any transaction in the East-Coast. In other words, he was looking for any customer from the West-Coast who rented a virtual machine for more hours than any customer from the East-Coast, but who paid less. Figure 1 illustrates a data instance for both tables. He wrote the following join query for such a task: