The Complexity of Resilience

One focus area in data management research is to understand how changes in the data can affect the output of a view or standing query. Example applications are explaining query results and propagating updates through views. In this thesis we study the complexity of the Resilience problem, which is the problem of finding the minimum number of tuples that need to be deleted from the database in order to change the result of a query. We will see that resilience is closely related to the well-studied problems of deletion propagation and causal responsibility, and that analyzing its complexity offers important insight for solving those problems as well. Our contributions include the definition of the concept of triads for conjunctive queries, which is a crucial tool on our analysis, and the characterization of a NP versus P dichotomy for the resilience problem considering the class of conjunctive queries without self-joins. Moreover, this result allowed us to show dichotomies for the same class of queries for both deletion propagation with source side-effects and causal responsibility problems. We also completely characterize how the presence of functional dependencies can change the complexity of such problems. The class of conjunctive queries with self-joins is far richer and more complicated than the self-join-free ones. Therefore we focus on binary queries without variable repetition, which are queries formed by unary or binary relations only and each atom has only one occurrence of any variable. For this restricted case, we identify three main query structures that help us identify complexity: chains, permutations and confluences. Using those we are able to characterize classes of queries for which resilience is NP-complete and some for which it is P

A Unified Approach for Resilience and Causal Responsibility with Integer Linear Programming (ILP) and LP Relaxations

Resilience is one of the key algorithmic problems underlying various forms of reverse data management (such as view maintenance, deletion propagation, and various interventions for fairness): What is the minimal number of tuples to delete from a database in order to remove all answers from a query? A long-open question is determining those conjunctive queries (CQs) for which this problem can be solved in guaranteed PTIME. We shed new light on this and the related problem of causal responsibility by proposing a unified Integer Linear Programming (ILP) formulation. It is unified in that it can solve both prior studied restrictions (e.g., self-join-free CQs under set semantics that allow a PTIME solution) and new cases (e.g., all CQs under set or bag semantics It is also unified in that all queries and all instances are treated with the same approach, and the algorithm is guaranteed to terminate in PTIME for the easy cases. We prove that, for all easy self-join-free CQs, the Linear Programming (LP) relaxation of our encoding is identical to the ILP solution and thus standard ILP solvers are guaranteed to return the solution in PTIME. Our approach opens up the door to new variants and new fine-grained analysis: 1) It also works under bag semantics and we give the first dichotomy result for bags semantics in the problem space. 2) We give a more fine-grained analysis of the complexity of causal responsibility. 3) We recover easy instances for generally hard queries, such as instances with read-once provenance and instances that become easy because of Functional Dependencies in the data. 4) We solve an open conjecture from PODS 2020. 5) Experiments confirm that our results indeed predict the asymptotic running times, and that our universal ILP encoding is at times even faster to solve for the PTIME cases than a prior proposed dedicated flow algorithm.Comment: 25 pages, 16 figure

Consistent Query Answering for Primary Keys on Rooted Tree Queries

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 self-join-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 $\cap$ 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).Comment: To appear in PODS'2

Computational Complexity And Algorithms For Dirty Data Evaluation And Repairing

In this dissertation, we study the dirty data evaluation and repairing problem in relational database. Dirty data is usually inconsistent, inaccurate, incomplete and stale. Existing methods and theories of consistency describe using integrity constraints, such as data dependencies. However, integrity constraints are good at detection but not at evaluating the degree of data inconsistency and cannot guide the data repairing. This dissertation first studies the computational complexity of and algorithms for the database inconsistency evaluation. We define and use the minimum tuple deletion to evaluate the database inconsistency. For such minimum tuple deletion problem, we study the relationship between the size of rule set and its computational complexity. We show that the minimum tuple deletion problem is NP-hard to approximate the minimum tuple deletion within 17/16 if given three functional dependencies and four attributes involved. A near optimal approximated algorithm for computing the minimum tuple deletion is proposed with a ratio of 2 − 1/2r , where r is the number of given functional dependencies. To guide the data repairing, this dissertation also investigates the data repairing method by using query feedbacks, formally studies two decision problems, functional dependency restricted deletion and insertion propagation problem, corresponding to the feedbacks of deletion and insertion. A comprehensive analysis on both combined and data complexity of the cases is provided by considering different relational operators and feedback types. We have identified the intractable and tractable cases to picture the complexity hierarchy of these problems, and provided the efficient algorithm on these tractable cases. Two improvements are proposed, one focuses on figuring out the minimum vertex cover in conflict graph to improve the upper bound of tuple deletion problem, and the other one is a better dichotomy for deletion and insertion propagation problems at the absence of functional dependencies from the point of respectively considering data, combined and parameterized complexities

Explain3D: Explaining Disagreements in Disjoint Datasets

Data plays an important role in applications, analytic processes, and many aspects of human activity. As data grows in size and complexity, we are met with an imperative need for tools that promote understanding and explanations over data-related operations. Data management research on explanations has focused on the assumption that data resides in a single dataset, under one common schema. But the reality of today's data is that it is frequently un-integrated, coming from different sources with different schemas. When different datasets provide different answers to semantically similar questions, understanding the reasons for the discrepancies is challenging and cannot be handled by the existing single-dataset solutions. In this paper, we propose Explain3D, a framework for explaining the disagreements across disjoint datasets (3D). Explain3D focuses on identifying the reasons for the differences in the results of two semantically similar queries operating on two datasets with potentially different schemas. Our framework leverages the queries to perform a semantic mapping across the relevant parts of their provenance; discrepancies in this mapping point to causes of the queries' differences. Exploiting the queries gives Explain3D an edge over traditional schema matching and record linkage techniques, which are query-agnostic. Our work makes the following contributions: (1) We formalize the problem of deriving optimal explanations for the differences of the results of semantically similar queries over disjoint datasets. (2) We design a 3-stage framework for solving the optimal explanation problem. (3) We develop a smart-partitioning optimizer that improves the efficiency of the framework by orders of magnitude. (4)~We experiment with real-world and synthetic data to demonstrate that Explain3D can derive precise explanations efficiently

RDF Data Indexing and Retrieval: A survey of Peer-to-Peer based solutions

The Semantic Web enables the possibility to model, create and query resources found on the Web. Enabling the full potential of its technologies at the Internet level requires infrastructures that can cope with scalability challenges and support various types of queries. The attractive features of the Peer-to-Peer (P2P) communication model such as decentralization, scalability, fault-tolerance seems to be a natural solution to deal with these challenges. Consequently, the combination of the Semantic Web and the P2P model can be a highly innovative attempt to harness the strengths of both technologies and come up with a scalable infrastructure for RDF data storage and retrieval. In this respect, this survey details the research works that adopt this combination and gives an insight on how to deal with the RDF data at the indexing and querying levels.Le Web Sémantique permet de modéliser, créer et faire des requêtes sur les ressources disponibles sur le Web. Afin de permettre à ses technologies d'exploiter leurs potentiels à l'échelle de l'Internet, il est nécessaire qu'elles reposent sur des infrastructures qui puissent passer à l'échelle ainsi que de répondre aux exigences d'expressivité des types de requêtes qu'elles offrent. Les bonnes propriétés qu'offrent les dernières générations de systèmes pair-à- pair en termes de décentralisation, de tolérance aux pannes ainsi que de passage à l'échelle en font d'eux des candidats prometteurs. La combinaison du modèle pair-à-pair et des technologies du Web Sémantique est une tentative innovante ayant pour but de fournir une infrastructure capable de passer à l'échelle et pouvant stocker et rechercher des données de type RDF. Dans ce contexte, ce rapport présente un état de l'art et discute en détail des travaux autour de systèmes pair-à-pair qui traitent des données de type RDF à large échelle. Nous détaillons leurs mécanismes d'indexation de données ainsi que le traitement des divers types de requêtes offerts