Yannakakis' seminal algorithm is optimal for acyclic joins, yet it has not been widely adopted due to its poor performance in practice. This paper briefly surveys recent advancements in making Yannakakis' algorithm more practical, in terms of both efficiency and ease of implementation, and points out several avenues for future research.

Most research on query optimization has centered on binary join algorithms like hash join and sort-merge join. However, recent years have seen growing interest in theoretically optimal algorithms, notably Yannakakis' algorithm. These algorithms rely on join trees, which differ from the operator trees for binary joins and require new optimization techniques. We propose three approaches to constructing join trees for acyclic queries. First, we give an algorithm to enumerate all join trees of an alpha-acyclic query by edits with amortized constant delay, which forms the basis of a cost-based optimizer for acyclic joins. Second, we show that the Maximum Cardinality Search algorithm by Tarjan and Yannakakis constructs a unique shallowest join tree, rooted at any relation, for a Berge-acyclic query; this tree enables parallel execution of large join queries. Finally, we prove that any connected left-deep linear plan for a gamma-acyclic query can be converted into a join tree by a simple algorithm, allowing reuse of optimization infrastructure developed for binary joins.

We present a novel linear-time acyclic join algorithm, TreeTracker Join ( TTJ ). The algorithm can be understood as the pipelined binary hash join with a simple twist: upon a hash lookup failure, TTJ resets execution to the binding of the tuple causing the failure, and removes the offending tuple from its relation. Compared to the best known linear-time acyclic join algorithm, Yannakakis’s algorithm, TTJ shares the same asymptotic complexity while imposing lower overhead. Further, we prove that when measuring query performance by counting the number of hash probes, TTJ will match or outperform binary hash join on the same plan. This property holds independently of the plan and independently of acyclicity. We are able to extend our theoretical results to cyclic queries by introducing a new hypergraph decomposition method called tree convolution. Tree convolution iteratively identifies and contracts acyclic subgraphs of the query hypergraph. The method avoids redundant calculations associated with tree decomposition and may be of independent interest. Empirical results on TPC-H, the Join Order Benchmark, and the Star Schema Benchmark demonstrate favorable results.

Recent work in programming languages developed an approach to term rewritings based on equality saturation (EqSat), which, instead of applying destructively the rewrite rules, maintains all equivalent expressions in a structure called an E-graph. This paper describes two surprising connections between EqSat and databases, going both ways. On one hand equality saturation can be viewed as a query evaluation problem, with great benefits. On the other hand, most sophisticated SQL query optimizers are based on the Volcano/Cascades framework which, we explain, is a variant of EqSat.

Equality saturation is an emerging technique for program and query optimization developed in the programming language community. It performs term rewriting over an E-graph, a data structure that compactly represents a program space. Despite its popularity, the theory of equality saturation lags behind the practice. In this paper, we define a fixpoint semantics of equality saturation based on tree automata and uncover deep connections between equality saturation and the chase. We characterize the class of chase sequences that correspond to equality saturation. We study the complexities of terminations of equality saturation in three cases: single-instance, all-term-instance, and all-E-graph-instance. Finally, we define a syntactic criterion based on acyclicity that implies equality saturation termination.

Acyclic join queries can be evaluated instance-optimally using Yannakakis' algorithm, which avoids needlessly large intermediate results through semi-join passes. Recent work proposes to address the significant hidden constant factors arising from a naive implementation of Yannakakis by decomposing the hash join operator into two suboperators, called Lookup and Expand. We present a novel method for integrating Lookup and Expand plans in interpreted environments, like column stores, formalizing them using Nested Semijoin Algebra (NSA) and implementing them through a shredding approach. We characterize the class of NSA expressions that can be evaluated instance-optimally as those that are 2-phase: no 'shrinking' operator is applied after an unnest (i.e., expand). We introduce Shredded Yannakakis (SYA), an evaluation algorithm for acyclic joins that, starting from a binary join plan, transforms it into a 2-phase NSA plan, and then evaluates it through the shredding technique. We show that SYA is provably robust (i.e., never produces large intermediate results) and without regret (i.e., is never worse than the binary join plan under a suitable cost model) on the class of well-behaved binary join plans. Our experiments on a suite of 1,849 queries show that SYA improves performance for 85.3% of the queries with speedups up to 62.5x, while remaining competitive on the other queries.

Over the last decade, worst-case optimal join (WCOJ) algorithms have emerged as a new paradigm for one of the most fundamental challenges in query processing: computing joins efficiently. Such an algorithm can be asymptotically faster than traditional binary joins, all the while remaining simple to understand and implement. However, they have been found to be less efficient than the old paradigm, traditional binary join plans, on the typical acyclic queries found in practice. Some database systems that support WCOJ use a hybrid approach: use WCOJ to process the cyclic subparts of the query (if any), and rely on traditional binary joins otherwise. In this paper we propose a new framework, called Free Join, that unifies the two paradigms. We describe a new type of plan, a new data structure (which unifies the hash tables and tries used by the two paradigms), and a suite of optimization techniques. Our system, implemented in Rust, matches or outperforms both traditional binary joins and WCOJ on standard query benchmarks.

Recursive queries have been traditionally studied in the framework of datalog, a language that restricts recursion to monotone queries over sets, which is guaranteed to converge in polynomial time in the size of the input. But modern big data systems require recursive computations beyond the Boolean space. In this paper we study the convergence of datalog when it is interpreted over an arbitrary semiring. We consider an ordered semiring, define the semantics of a datalog program as a least fixpoint in this semiring, and study the number of steps required to reach that fixpoint, if ever. We identify algebraic properties of the semiring that correspond to certain convergence properties of datalog programs. Finally, we describe a class of ordered semirings on which one can use the semi-naive evaluation algorithm on any datalog program.

Most work on query optimization has concentrated on loop-free queries. However, data science and machine learning workloads today typically involve recursive or iterative computation. In this work, we propose a novel framework for optimizing recursive queries using methods from program synthesis. In particular, we introduce a simple yet powerful optimization rule called the "FGH-rule" which aims to find a faster way to evaluate a recursive program. The solution is found by making use of powerful tools, such as a program synthesizer, an SMT-solver, and an equality saturation system. We demonstrate the strength of the optimization by showing that the FGH-rule can lead to speedups up to 4 orders of magnitude on three, already optimized Datalog systems.