skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Friday, April 12 until 2:00 AM ET on Saturday, April 13 due to maintenance. We apologize for the inconvenience.


Title: Optimal Join Algorithms Meet Top-k
Top-k queries have been studied intensively in the database community and they are an important means to reduce query cost when only the “best” or “most interesting” results are needed instead of the full output. While some optimality results exist, e.g., the famous Threshold Algorithm, they hold only in a fairly limited model of computation that does not account for the cost incurred by large intermediate results and hence is not aligned with typical database-optimizer cost models. On the other hand, the idea of avoiding large intermediate results is arguably the main goal of recent work on optimal join algorithms, which uses the standard RAM model of computation to determine algorithm complexity. This research has created a lot of excitement due to its promise of reducing the time complexity of join queries with cycles, but it has mostly focused on full-output computation. We argue that the two areas can and should be studied from a unified point of view in order to achieve optimality in the common model of computation for a very general class of top-k-style join queries. This tutorial has two main objectives. First, we will explore and contrast the main assumptions, concepts, and algorithmic achievements of the two research areas. Second, we will cover recent, as well as some older, approaches that emerged at the intersection to support efficient ranked enumeration of join-query results. These are related to classic work on k-shortest path algorithms and more general optimization problems, some of which dates back to the 1950s. We demonstrate that this line of research warrants renewed attention in the challenging context of ranked enumeration for general join queries.  more » « less
Award ID(s):
1762268 1956096
NSF-PAR ID:
10225414
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
SIGMOD 2020
Page Range / eLocation ID:
2659 to 2665
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes seemingly different problems that had been studied in isolation. To this end, we extend classic algorithms that find the k -shortest paths in a weighted graph. For full conjunctive queries, including cyclic ones, our approach is optimal in terms of the time to return the top result and the delay between results. These optimality properties are derived for the widely used notion of data complexity, which treats query size as a constant. By performing a careful cost analysis, we are able to uncover a previously unknown tradeoff between two incomparable enumeration approaches: one has lower complexity when the number of returned results is small, the other when the number is very large. We theoretically and empirically demonstrate the superiority of our techniques over batch algorithms, which produce the full result and then sort it. Our technique is not only faster for returning the first few results, but on some inputs beats the batch algorithm even when all results are produced. 
    more » « less
  2. We study theta-joins in general and join predicates with conjunctions and disjunctions of inequalities in particular, focusing on ranked enumeration where the answers are returned incrementally in an order dictated by a given ranking function. Our approach achieves strong time and space complexity properties: with n denoting the number of tuples in the database, we guarantee for acyclic full join queries with inequality conditions that for every value of k , the k top-ranked answers are returned in O ( n polylog n + k log k ) time. This is within a polylogarithmic factor of O ( n + k log k ), i.e., the best known complexity for equi-joins, and even of O ( n + k ), i.e., the time it takes to look at the input and return k answers in any order. Our guarantees extend to join queries with selections and many types of projections (namely those called "free-connex" queries and those that use bag semantics). Remarkably, they hold even when the number of join results is n ℓ for a join of ℓ relations. The key ingredient is a novel O ( n polylog n )-size factorized representation of the query output , which is constructed on-the-fly for a given query and database. In addition to providing the first nontrivial theoretical guarantees beyond equi-joins, we show in an experimental study that our ranked-enumeration approach is also memory-efficient and fast in practice, beating the running time of state-of-the-art database systems by orders of magnitude. 
    more » « less
  3. Join query evaluation with ordering is a fundamental data processing task in relational database management systems. SQL and custom graph query languages such as Cypher offer this functionality by allowing users to specify the order via the ORDER BY clause. In many scenarios, the users also want to see the first k results quickly (expressed by the LIMIT clause), but the value of k is not predetermined as user queries are arriving in an online fashion. Recent work has made considerable progress in identifying optimal algorithms for ranked enumeration of join queries that do not contain any projections. In this paper, we initiate the study of the problem of enumerating results in ranked order for queries with projections. Our main result shows that for any acyclic query, it is possible to obtain a near-linear (in the size of the database) delay algorithm after only a linear time preprocessing step for two important ranking functions: sum and lexicographic ordering. For a practical subset of acyclic queries known as star queries, we show an even stronger result that allows a user to obtain a smooth tradeoff between faster answering time guarantees using more preprocessing time. Our results are also extensible to queries containing cycles and unions. We also perform a comprehensive experimental evaluation to demonstrate that our algorithms, which are simple to implement, improve up to three orders of magnitude in the running time over state-of-the-art algorithms implemented within open-source RDBMS and specialized graph databases. 
    more » « less
  4. In the last few years, much effort has been devoted to developing join algorithms to achieve worst-case optimality for join queries over relational databases. Towards this end, the database community has had considerable success in developing efficient algorithms that achieve worst-case optimal runtime for full join queries, i.e., joins without projections. However, not much is known about join evaluation with projections beyond some simple techniques of pushing down the projection operator in the query execution plan. Such queries have a large number of applications in entity matching, graph analytics and searching over compressed graphs. In this paper, we study how a class of join queries with projections can be evaluated faster using worst-case optimal algorithms together with matrix multiplication. Crucially, our algorithms are parameterized by the output size of the final result, allowing for choosing the best execution strategy. We implement our algorithms as a subroutine and compare the performance with state-of-the-art techniques to show they can be improved upon by as much as 50x. More importantly, our experiments indicate that matrix multiplication is a useful operation that can help speed up join processing owing to highly optimized open-source libraries that are also highly parallelizable. 
    more » « less
  5. Tuple-independent probabilistic databases (TI-PDBs) han- dle uncertainty by annotating each tuple with a probability parameter; when the user submits a query, the database de- rives the marginal probabilities of each output-tuple, assum- ing input-tuples are statistically independent. While query processing in TI-PDBs has been studied extensively, limited research has been dedicated to the problems of updating or deriving the parameters from observations of query results . Addressing this problem is the main focus of this paper. We introduce Beta Probabilistic Databases (B-PDBs), a general- ization of TI-PDBs designed to support both (i) belief updat- ing and (ii) parameter learning in a principled and scalable way. The key idea of B-PDBs is to treat each parameter as a latent, Beta-distributed random variable. We show how this simple expedient enables both belief updating and pa- rameter learning in a principled way, without imposing any burden on regular query processing. We use this model to provide the following key contributions: (i) we show how to scalably compute the posterior densities of the parameters given new evidence; (ii) we study the complexity of perform- ing Bayesian belief updates, devising efficient algorithms for tractable classes of queries; (iii) we propose a soft-EM algo- rithm for computing maximum-likelihood estimates of the parameters; (iv) we show how to embed the proposed algo- rithms into a standard relational engine; (v) we support our conclusions with extensive experimental results. 
    more » « less