We study the data complexity of consistent query answering (CQA) on databases that may violate the primary key constraints. A repair is a maximal subset of the database satisfying the primary key constraints. For a Boolean query q, the problem CERTAINTY(q) takes a database as input, and asks whether or not each repair satisfies q. The computational complexity of CERTAINTY(q) has been established whenever q is a selfjoin-free Boolean conjunctive query, or a (not necessarily self-join-free) Boolean path query. In this paper, we take one more step towards a general classification for all Boolean conjunctive queries by considering the class of rooted tree queries. In particular, we show that for every rooted tree query q, CERTAINTY(q) is in FO, NL-hard ∩ LFP, or coNP-complete, and it is decidable (in polynomial time), given q, which of the three cases applies. We also extend our classification to larger classes of queries with simple primary keys. Our classification criteria rely on query homomorphisms and our polynomial-time fixpoint algorithm is based on a novel use of context-free grammar (CFG).
The unit interval vertex deletion problem asks for a set of at most k vertices whose deletion from an n-vertex graph makes it a unit interval graph. We develop an O(k 4 )-vertex kernel for the problem, significantly improving the O(k 53 )-vertex kernel of Fomin, Saurabh, and Villanger [ESA'12; SIAM J. Discrete Math 27 (2013)]. We introduce a novel way of organizing cliques of a unit interval graph. Our constructive proof for the correctness of our algorithm, using interval models, greatly simplifies the destructive proofs, based on forbidden induced subgraphs, for similar problems in literature.
Most data analytical pipelines often encounter the problem of querying inconsistent data that violate pre-determined integrity constraints. Data cleaning is an extensively studied paradigm that singles out a consistent repair of the inconsistent data. Consistent query answering (CQA) is an alternative approach to data cleaning that asks for all tuples guaranteed to be returned by a given query on all (in most cases, exponentially many) repairs of the inconsistent data. In this paper, we identify a class of acyclic select-project-join (SPJ) queries for which CQA can be solved via SQL rewriting with a linear time guarantee. Our rewriting method can be viewed as a generalization of Yannakakis' algorithm for acyclic joins to the inconsistent setting. We present LinCQA, a system that takes as input any query in our class and outputs rewritings in both SQL and non-recursive Datalog with negation. We show that LinCQA often outperforms the existing CQA systems on both synthetic and real-world workloads, and in some cases, by orders of magnitude.
Today cloud companies offer fully managed Spark services. This has made it easy to onboard new customers but has also increased the volume of users and their workload sizes. However, both cloud providers and users lack the tools and time to optimize these massive workloads. To solve this problem, we designed SparkCruise that can help understand and optimize workload instances by adding a workload-driven feedback loop to the Spark query optimizer. In this paper, we present our approach to collecting and representing Spark query workloads and use it to improve the overall performance on the workload, all without requiring any access to user data. These methods scale with the number of workloads and apply learned feedback in an online fashion. We explain one specific workload optimization developed for computation reuse. We also share the detailed analysis of production Spark workloads and contrast them with the corresponding analysis of TPC-DS benchmark. To the best of our knowledge, this is the first study to share the analysis of large-scale production Spark SQL workloads.
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