Optimization of a subclass of conjunctive queries

The optimization problem for a subclass of conjunctive queries which is formed by the union of the class of fan-out free queries and a subclass of typed fan-out queries is investigated. The typed fan-out queries in this class are obtained from simple tableaux by allowing atmost one attribute to violate the simple-tablau property. The optimization problem for several restricted subsets of typed fan-out queries is already known to be NP-hard. It is shown that the queries under consideration possess several useful properties which are then used to obtain an O(n ²) optimization algorithm based on the implication graph technique. The optimization of typed fan-out queries, obtained from simple tableaux by allowing atmost two attributes to violate the simple tableau property, is shown to be NP-hard. The optimization of simple tableaux in the presence of functional dependencies is also investigated and is shown to be NP-hard.Supported by DFG grant Bi 311/1-2; present address: School of Computer & Systems Sciences, Jawaharlal Nehru University, New Delhi 110067, India.Supported by NSF grant IRI-87-22886, AFOSR grant 88-0266 and a grant from IBM Corp.     

On the non-efficient PAC learnability of conjunctive queries

This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting property, a property that is tacitly assumed in much of the computational learning theory literature; (ii) we establish a strong negative PAC learnability result that applies to many restricted classes of conjunctive queries (CQs), including acyclic CQs for a wide range of notions of acyclicity; (iii) we show that CQs (and UCQs) are efficiently PAC learnable with membership queries.     

Mapping-equivalence and oid-equivalence of single-function object-creating conjunctive queries

Conjunctive database queries have been extended with a mechanism for object creation to capture important applications such as data exchange, data integration, and ontology-based data access. Object creation generates new object identifiers in the result that do not belong to the set of constants in the source database. The new object identifiers can be also seen as Skolem terms. Hence, object-creating conjunctive queries can also be regarded as restricted second-order tuple-generating dependencies (SO-tgds), considered in the data exchange literature. In this paper, we focus on the class of single-function object-creating conjunctive queries, or sifo CQs for short. The single-function symbol can be used only once in the head of the query. We give a new characterization for oid-equivalence of sifo CQs that is simpler than the one given by Hull and Yoshikawa and places the problem in the complexity class NP. Our characterization is based on Cohen’s equivalence notions for conjunctive queries with multiplicities. We also solve the logical entailment problem for sifo CQs, showing that also this problem belongs to NP. Results by Pichler et al. have shown that logical equivalence for more general classes of SO-tgds is either undecidable or decidable with as yet unknown complexity upper bounds.     

Semantic Web search based on ontological conjunctive queries

Many experts predict that the next huge step forward in Web information technology will be achieved by adding semantics to Web data, and will possibly consist of (some form of) the Semantic Web. In this paper, we present a novel approach to Semantic Web search, called Serene, which allows for a semantic processing of Web search queries, and for evaluating complex Web search queries that involve reasoning over the Web. More specifically, we first add ontological structure and semantics to Web pages, which then allows for both attaching a meaning to Web search queries and Web pages, and for formulating and processing ontology-based complex Web search queries (i.e., conjunctive queries) that involve reasoning over the Web. Here, we assume the existence of an underlying ontology (in a lightweight ontology language) relative to which Web pages are annotated and Web search queries are formulated. Depending on whether we use a general or a specialized ontology, we thus obtain a general or a vertical Semantic Web search interface, respectively. That is, we are actually mapping the Web into an ontological knowledge base, which then allows for Semantic Web search relative to the underlying ontology. The latter is then realized by reduction to standard Web search on standard Web pages and logically completed ontological annotations. That is, standard Web search engines are used as the main inference motor for ontology-based Semantic Web search. We develop the formal model behind this approach and also provide an implementation in desktop search. Furthermore, we report on extensive experiments, including an implemented Semantic Web search on the Internet Movie Database.     

The complexity of weighted counting for acyclic conjunctive queries

This paper is a study of weighted counting of the solutions of acyclic conjunctive queries (ACQ). The unweighted quantifier free version of this problem is known to be tractable (for combined complexity), but it is also known that introducing even a single quantified variable makes it #P$\mathrm{\#}\mathsf{P}$-hard. We first show that weighted counting for quantifier free ACQ is still tractable and that even minimalistic extensions of the problem lead to hard cases. We then introduce a new parameter for quantified queries that permits to isolate a large island of tractability. We show that, up to a standard assumption from parameterized complexity, this parameter fully characterizes tractable subclasses for counting weighted solutions for ACQs. Thus we completely determine the tractability frontier for weighted counting for ACQ.     

Mining frequent conjunctive queries using functional and inclusion dependencies

We address the issue of mining frequent conjunctive queries in a relational database, a problem known to be intractable even for conjunctive queries over a single table. In this article, we show that mining frequent projection-selection-join queries becomes tractable if joins are performed along keys and foreign keys, in a database satisfying functional and inclusion dependencies, under certain restrictions. We note that these restrictions cover most practical cases, including databases operating over star schemas, snow-flake schemas and constellation schemas. In our approach, we define an equivalence relation over queries using a pre-ordering with respect to which the support is shown to be anti-monotonic. We propose a level-wise algorithm for computing all frequent queries by exploiting the fact that equivalent queries have the same support. We report on experiments showing that, in our context, mining frequent projection-selection-join queries is indeed tractable, even for large data sets.     

Determinacy and query rewriting for conjunctive queries and views

Answering queries using views is the problem which examines how to derive the answers to a query when we only have the answers to a set of views. Constructing rewritings is a widely studied technique to derive those answers. In this paper we consider the problem of the existence of rewritings in the case where the answers to the views uniquely determine the answers to the query. Specifically, we say that a view set Vdetermines a query Q if for any two databases D₁,D₂ it holds: V(D₁)=V(D₂) implies Q(D₁)=Q(D₂). We consider the case where query and views are defined by conjunctive queries and investigate the question: If a view set V determines a query Q, is there an equivalent rewriting of Q using V? We present here interesting cases where there are such rewritings in the language of conjunctive queries. Interestingly, we identify a class of conjunctive queries, CQ_path, for which a view set can produce equivalent rewritings for “almost all” queries which are determined by this view set. We introduce a problem which relates determinacy to query equivalence. We show that there are cases where restricted results can carry over to broader classes of queries.     

Mining frequent conjunctive queries in relational databases through dependency discovery

We present an approach for mining frequent conjunctive in arbitrary relational databases. Our pattern class is the simple, but appealing subclass of simple conjunctive queries. Our algorithm, called Conqueror $^+$ , is capable of detecting previously unknown functional and inclusion dependencies that hold on the database relations as well as on joins of relations. These newly detected dependencies are then used to prune redundant queries. We propose an efficient database-oriented implementation of our algorithm using SQL and provide several promising experimental results.     

Verifiable searchable symmetric encryption for conjunctive keyword queries in cloud storage

Searchable symmetric encryption (SSE) has been introduced for secure outsourcing the encrypted database to cloud storage, while maintaining searchable features. Of various SSE schemes, most of them assume the server is honest but curious, while the server may be trustless in the real world. Considering a malicious server not honestly performing the queries, verifiable SSE (VSSE) schemes are constructed to ensure the verifiability of the search results. However, existing VSSE constructions only focus on single-keyword search or incur heavy computational cost during verification. To address this challenge, we present an efficient VSSE scheme, built on OXT protocol (Cash et al., CRYPTO 2013), for conjunctive keyword queries with sublinear search overhead. The proposed VSSE scheme is based on a privacy-preserving hash-based accumulator, by leveraging a well-established cryptographic primitive, Symmetric Hidden Vector Encryption (SHVE). Our VSSE scheme enables both correctness and completeness verifiability for the result without pairing operations, thus greatly reducing the computational cost in the verification process. Besides, the proposed VSSE scheme can still provide a proof when the search result is empty. Finally, the security analysis and experimental evaluation are given to demonstrate the security and practicality of the proposed scheme.     

Optimal schema hierarchies in searching semistructured databases by conjunctive regular path queries

An approach to estimating effectiveness of index usage when searching semistructured databases consisting of OEM documents is presented. In addition to the estimation of the hierarchy optimality from the standpoint of calculation of conjunctive regular path queries, this approach allows one to take into account arbitrary distributions of query probabilities. Algorithms for index construction are given, and estimates of their complexity are obtained. These estimates clearly demonstrate efficiency of the approach and practical applicability of the algorithms suggested.     

Measuring similarity of individuals in description logics over the refinement space of conjunctive queries

Sensor networks, communication and financial networks, web and social networks are becoming increasingly important in our day-to-day life. They contain entities which may interact with one another. These interactions are often characterized by a form of autocorrelation, where the value of an attribute at a given entity depends on the values at the entities it is interacting with. In this situation, the collective inference paradigm offers a unique opportunity to improve the performance of predictive models on network data, as interacting instances are labeled simultaneously by dealing with autocorrelation. Several recent works have shown that collective inference is a powerful paradigm, but it is mainly developed with a fully-labeled training network. In contrast, while it may be cheap to acquire the network topology, it may be costly to acquire node labels for training. In this paper, we examine how to explicitly consider autocorrelation when performing regression inference within network data. In particular, we study the transduction of collective regression when a sparsely labeled network is a common situation. We present an algorithm, called CORENA (COllective REgression in Network dAta), to assign a numeric label to each instance in the network. In particular, we iteratively augment the representation of each instance with instances sharing correlated representations across the network. In this way, the proposed learning model is able to capture autocorrelations of labels over a group of related instances and feed-back the more reliable labels predicted by the transduction in the labeled network. Empirical studies demonstrate that the proposed approach can boost regression performances in several spatial and social tasks.     

View selection for <Emphasis Type="Italic">real</Emphasis> conjunctive queries

Given a query workload, a database and a set of constraints, the view-selection problem is to select views to materialize so that the constraints are satisfied and the views can be used to compute the queries in the workload efficiently. A typical constraint, which we consider in the present work, is to require that the views can be stored in a given amount of disk space. Depending on features of SQL queries (e.g., the DISTINCT keyword) and on whether the database relations on which the queries are applied are sets or bags, the queries may be computed under set semantics, bag-set semantics, or bag semantics. In this paper we study the complexity of the view-selection problem for conjunctive queries and views under these semantics. We show that bag semantics is the “easiest to handle” (we show that in this case the decision version of view selection is in NP), whereas under set and bag-set semantics we assume further restrictions on the query workload (we only allow queries without self-joins in the workload) to achieve the same complexity. Moreover, while under bag and bag-set semantics filtering views (i.e., subgoals that can be dropped from the rewriting without impacting equivalence to the query) are practically not needed, under set semantics filtering views can reduce significantly the query-evaluation costs. We show that under set semantics the decision version of the view-selection problem remains in NP only if filtering views are not allowed in the rewritings. Finally, we investigate whether the cgalg algorithm for view selection introduced in Chirkova and Genesereth (Linearly bounded reformulations of conjunctive databases, pp. 987–1001, 2000) is suitable in our setting. We prove that this algorithm is sound for all cases we examine here, and that it is complete under bag semantics for workloads of arbitrary conjunctive queries and under bag-set semantics for workloads of conjunctive queries without self-joins. Rada Chirkova’s work on this material has been supported by the National Science Foundation under Grant No. 0307072. The project is co-funded by the European Social Fund (75%) and National Resources (25%)- Operational Program for Educational and Vocational Training II (EPEAEK II) and particularly the program PYTHAGORAS. A preliminary version of this paper appears in F. Afrati, R. Chirkova, M. Gergatsoulis, V. Pavlaki. Designing Views to Efficiently Answer Real SQL Queries. In Proc. of SARA 2005, LNAI Vol. 3607, pages 332-346, Springer-Verlag, 2005.     

Mining conjunctive sequential patterns

In this paper we aim at extending the non-derivable condensed representation in frequent itemset mining to sequential pattern mining. We start by showing a negative example: in the context of frequent sequences, the notion of non-derivability is meaningless. Therefore, we extend our focus to the mining of conjunctions of sequences. Besides of being of practical importance, this class of patterns has some nice theoretical properties. Based on a new unexploited theoretical definition of equivalence classes for sequential patterns, we are able to extend the notion of a non-derivable itemset to the sequence domain. We present a new depth-first approach to mine non-derivable conjunctive sequential patterns and show its use in mining association rules for sequences. This approach is based on a well known combinatorial theorem: the Möbius inversion. A performance study using both synthetic and real datasets illustrates the efficiency of our mining algorithm. These new introduced patterns have a high-potential for real-life applications, especially for network monitoring and biomedical fields with the ability to get sequential association rules with all the classical statistical metrics such as confidence, conviction, lift etc.     

Planning for conjunctive goals

The problem of achieving conjunctive goals has been central to domain-independent planning research; the nonlinear constraint-posting approach has been most successful. Previous planners of this type have been complicated, heuristic, and ill-defined. I have combined and distilled the state of the art into a simple, precise, implemented algorithm (TWEAK) which I have proved correct and complete. I analyze previous work on domain-independent conjunctive planning; in retrospect it becomes clear that all conjunctive planners, linear and nonlinear, work the same way. The efficiency and correctness of these planners depends on the traditional add/delete-list representation for actions, which drastically limits their usefulness. I present theorems that suggest that efficient general purpose planning with more expressive action representations is impossible, and suggest ways to avoid this problem.     

支持连接关键词搜索的属性加密方案研究

基于属性的加密机制能够实现细粒度的访问控制,支持多用户数据共享.针对大部分基于属性的可搜索加密方案存在效率低下、密钥易泄露以及仅支持单关键词搜索的问题,提出了一个支持连接关键词搜索的属性加密方案.该方案采用线性秘密共享矩阵实现访问控制,将秘密共享和恢复操作在一个与参与方属性关联的矩阵中进行,通过矩阵运算减少了计算量.在...     

The hardest linear conjunctive language

This paper demonstrates that the P-complete language of yes-instances of Circuit Value Problem under a suitable encoding can be generated by a linear conjunctive grammar, or, equivalently, accepted by a triangular trellis automaton. This result has several implications on the properties of the languages generated by conjunctive grammars of the general form and on the relationship between the abstract models of parallel computation.     

Buffer queries

A class of commonly asked queries in a spatial database is known as buffer queries. An example of such a query is to "find house-power line pairs that are within 50 meters of each other." A buffer query involves two spatial data sets and a distance d. The answer to this query are pairs of objects, one from each input set, that are within distance d of each other. Given nonpoint spatial objects, evaluation of buffer queries could be a costly operation, even when the numbers of objects in the input data sets are relatively small. This paper addresses the problem of how to evaluate this class of queries efficiently. A fundamental problem with buffer query evaluation is to find an efficient algorithm for solving the minimum distance (miniDist) problem for lines and regions. An efficient minDist algorithm, which only requires a subsequence of segments from each object to be examined, is derived. Finding a fast minDist algorithm is the first step in evaluating a buffer query efficiently. It is observed that many, and sometimes even most, candidates can be proven in the answer without resorting to the relatively expensive minDist operation. A candidate is first evaluated with a least expensive technique-called O-object filtering. If it fails, a more costly operation, called 1-object filtering, is applied. Finally, if both filterings fail, the most expensive minDist algorithm is invoked. To show the effectiveness of the these techniques, they are incorporated into the well-known tree join algorithm and tested with real-life as well as artificial data sets. Extensive experiments show that the proposed algorithm outperforms existing techniques by a wide margin in both execution time as well as IO accesses. More importantly, the performance gain improves drastically with the increase of distance values.