Adding a path connectedness operator to FO+poly (linear)

In the constraint database community FO+poly and FO+linear have been proposed as foundations for spatial database query languages. One of the strengths of this approach is that these languages are a clean and natural generalization of Codd's relational model to a spatial setting. As a result rigorous mathematical study of their expressiveness and complexity can be carried out. Along this line important geometric queries involving connectivity have been shown to be inexpressible in FO+poly and FO+linear. To address this problem we extend both languages with a parameterized path-connectivity predicate Pconn. We show that FO+linear+Pconn and FO+poly+Pconn[3D] are closed and have PTIME data complexity. We also examine the expressiveness of FO+poly+Pconn and FO+linear+Pconn and show that parity and transitive closure are expressible in each. Received: 8 January 2001 / 22 February 2002     

Regular path queries under approximate semantics

We give a general framework for approximate query processing in semistructured databases. We focus on regular path queries, which are the integral part of most of the query languages for semistructured databases. To enable approximations, we allow the regular path queries to be distorted. The distortions are expressed in the system by using weighted regular expressions, which correspond to weighted regular transducers. After defining the notion of weighted approximate answers we show how to compute them in order of their proximity to the query. In the new approximate setting, query containment has to be redefined in order to take into account the quantitative proximity information in the query answers. For this, we define the approximate containment, and its variants k-containment and reliable contain-ment. Then, we give an optimal algorithm for deciding the k-containment. Regarding the reliable approximate containment, we show that it is polynomial time equivalent to the notorious limitedness problem in distance automata.     

An expressive language for linear spatial database queries

We exhibit a coordinate-based language, called PFOL, which is sound for the linear queries computable in first-order logic over the reals and extends the latter's restriction to linear arithmetic. To evaluate its expressive power, we first consider PFOL-finite, the PFOL programs that compute finite outputs upon finite inputs. In order to study this fragment of PFOL, we also define an equivalent syntactical language, called SPFOL. We show that SPFOL has the same expressive power as SafeEuql (S. Cluet, R. Hull (Eds.), Proceedings of the Sixth International Workshop on Database Programming Languages, Lecture Notes in Computer Science, Vol. 1369, Springer, Berlin, 1997, pp. 1-24), whence all ruler-and-compass constructions in the plane on finite sets of points can be expressed in SPFOL. This result gives a geometrical justification of SPFOL, and, hence, also of PFOL-finite. Then, we define finite representations for arbitrary semi-linear sets and show that there are PFOL programs for both the encoding and the decoding. This result is used (i) to identify a broad, natural class of FO+poly-expressible linear queries of which we show equivalence with the class of PFOL-expressible queries, and (ii) to establish a general theorem about lifting query languages on finite databases to query languages on arbitrary linear databases. This theorem is applied to a recent result of Benedikt and Libkin (SIAM J. Comput. 29 (2000) 1652-1682) from finite to arbitrary semi-linear sets, yielding the existence of a natural, syntactically definable fragment of FO+poly sound and complete for all FO+poly-expressible linear queries.     

Answering reachability queries with ordered label constraints over labeled graphs

Reachability query plays a vital role in many graph analysis tasks. Previous researches proposed many methods to efficiently answer reachability queries between vertex pairs. Since many real graphs are labeled graph, it highly demands Label-Constrained Reachability (LCR) query in which constraint includes a set of labels besides vertex pairs. Recent researches proposed several methods for answering some LCR queries which require appearance of some labels specified in constraints in the path. Besides that constraint may be a label set, query constraint may be ordered labels, namely OLCR (Ordered-Label-Constrained Reachability) queries which retrieve paths matching a sequence of labels. Currently, no solutions are available for OLCR. Here, we propose DHL, a novel bloom filter based indexing technique for answering OLCR queries. DHL can be used to check reachability between vertex pairs. If the answers are not no, then constrained DFS is performed. So, we employ DHL followed by performing constrained DFS to answer OLCR queries. We show that DHL has a bounded false positive rate, and it’s powerful in saving indexing time and space. Extensive experiments on 10 real-life graphs and 12 synthetic graphs demonstrate that DHL achieves about 4.8–22.5 times smaller index space and 4.6–114 times less index construction time than two state-of-art techniques for LCR queries, while achieving comparable query response time. The results also show that our algorithm can answer OLCR queries effectively.     

Knowledge Compilation Meets Database Theory: Compiling Queries to Decision Diagrams

The goal of Knowledge Compilation is to represent a Boolean expression in a format in which it can answer a range of “online-queries” in PTIME. The online-query of main interest to us is model counting, because of its application to query evaluation on probabilistic databases, but other online-queries can be supported as well such as testing for equivalence, testing for implication, etc. In this paper we study the following problem: given a database query q, decide whether its lineage can be compiled efficiently into a given target language. We consider four target languages, of strictly increasing expressive power (when the size of compilation is restricted to be polynomial in the data size): read-once Boolean formulae, OBDD, FBDD and d-DNNF. For each target, we study the class of database queries that admit polynomial size representation: these queries can also be evaluated in PTIME over probabilistic databases. When queries are restricted to conjunctive queries without self-joins, it was known that these four classes collapse to the class of hierarchical queries, which is also the class of PTIME queries over probabilistic databases. Our main result in this paper is that, in the case of Unions of Conjunctive Queries (UCQ), these classes form a strict hierarchy. Thus, unlike conjunctive queries without self-joins, the expressive power of UCQ differs considerably with respect to these target compilation languages. Moreover, we give a complete characterization of the first two target languages, based on the query’s syntax.     

Aggregate Operators in Constraint Query Languages

We investigate the problem of how to extend constraint query languages with aggregate operators. We deal with standard relational aggregation, and also with aggregates specific to spatial data, such as volume. We study several approaches, including the addition of a new class of approximate aggregate operators which allow an error tolerance in the computation. We show how techniques of M. Karpinski and A. Macintyre (in “Structures in Logic and Computer Science: A Selection of Essays in Honor of A. Ehrenfeucht,” Springer Lecture Notes on Computer Science 1261, pp. 162–173, Springer-Verlag, Berlin, 1997) and P. Koiran (in “FOCS '95,” pp. 134–141) based on VC-dimension can be used to give languages with approximation operators, but also show that these languages have a number of shortcomings. We then give a set of results showing that it is impossible to get constraint-based languages that admit definable aggregation operators, both for exact operators and for approximate ones. These results are quite robust, in that they show that closure under aggregation is problematic even when the class of functions permitted in constraints is expanded. This motivates a different approach to the aggregation problem. We introduce a language FO+Poly+Sum, which permits standard discrete aggregation operators to be applied to the outputs of range-restricted constraint queries. We show that this language has a number of attractive closure and expressivity properties, and that it can compute volumes of linear-constraint databases.     

On the decidability of termination of query evaluation in transitive-closure logics for polynomial constraint databases

The formalism of constraint databases, in which possibly infinite data sets are described by Boolean combinations of polynomial inequality and equality constraints, has its main application area in spatial databases. The standard query language for polynomial constraint databases is first-order logic over the reals. Because of the limited expressive power of this logic with respect to queries that are important in spatial data base applications, various extensions have been introduced. We study extensions of first-order logic with different types of transitive-closure operators and we are in particular interested in deciding the termination of the evaluation of queries expressible in these transitive-closure logics. It turns out that termination is undecidable in general. However, we show that the termination of the transitive closure of a continuous function graph in the two-dimensional plane, viewed as a binary relation over the reals, is decidable, and even expressible in first-order logic over the reals. Based on this result, we identify a particular transitive-closure logic for which termination of query evaluation is decidable and which is more expressive than first-order logic over the reals. Furthermore, we can define a guarded fragment in which exactly the terminating queries of this language are expressible.     

Answering pattern match queries in large graph databases via graph embedding

The growing popularity of graph databases has generated interesting data management problems, such as subgraph search, shortest path query, reachability verification, and pattern matching. Among these, a pattern match query is more flexible compared with a subgraph search and more informative compared with a shortest path or a reachability query. In this paper, we address distance-based pattern match queries over a large data graph G. Due to the huge search space, we adopt a filter-and-refine framework to answer a pattern match query over a large graph. We first find a set of candidate matches by a graph embedding technique and then evaluate these to find the exact matches. Extensive experiments confirm the superiority of our method.     

Weighted path queries on semistructured databases

Path queries have been extensively used to query semistructured data, such as the Web and XML documents. In this paper we introduce weighted path queries, an extension of path queries enabling several classes of optimization problems (such as the computation of shortest paths) to be easily expressed. Weighted path queries are based on the notion of weighted regular expression, i.e., a regular expression whose symbols are associated to a weight. We characterize the problem of answering weighted path queries and provide an algorithm for computing their answer. We also show how weighted path queries can be effectively embedded into query languages for XML data to express in a simple and compact form several meaningful research problems.     

Incomplete deductive databases

We investigate the complexity of query processing in databases which have both incompletely specified data and deductive rules. The paper is divided into two parts: in the first we consider databases in which incompletely specified data occurs only in the database intension; in the second we consider databases in which incomplete information is represented only in database extension. We prove that, in general, the query processing problem for databases with incomplete intensions is undecidable. A number of classes of rules for which all conjunctive queries can be processed in polynomial time is then characterized. For databases with incomplete extensions we prove a number of CoNP completeness results. For instance, we demonstrate that processing disjunctions which are restricted to individual columns of database predicates can, in general, be as bad as processing arbitrary disjunctions (i.e. CoNP-complete). This falsifies the conjecture that such limited disjunctions could be computationally beneficial. We also show two simple examples of situations in which query processing is guaranteed to be polynomial. These situations are linked to certain assumptions about database updates.Finally, we provide a summary of the data complexity of queries depending on the type of database extension, intension, query sublanguage and Open World vs Closed World assumption.Research supported by NSF grant DCR 85-04140.More precisely, we can say this only in the presence of the closed world assumption [18].     

RQL: a recursive query language

Different classes of recursive queries in the relational databases are identified. It is shown that existing proposals to extend the relational query languages are either not powerful enough to express queries in many of these classes or use nonfirst normal form constructs. RQL, a recursive database query language that can be used to express recursive queries on all the classes identified, is presented. RQL is based on the relational algebra. In addition to functions that correspond to the standard and extended relational algebra operators, RQL supports functions required to express general recursive queries. The elements of RQL and the ways in which they are used to formulate complicated, but useful, recursive queries are described. The effects of the extensions embodied in RQL on the termination of recursive query evaluation are discussed     

Toward Practical Query Evaluation for Constraint Databases

Linear constraint databases (LCDBs) extend relational databases to include linear arithmetic constraints in both relations and queries. A LCDB can also be viewed as a powerful extension of linear programming (LP) where the system of constraints is generalized to a database containing constraints and the objective function is generalized to a relational query containing constraints. Our major concern is query optimization in LCDBs. Traditional database approaches are not adequate for combination with LP technology. Instead, we propose a new query optimization approach, based on statistical estimations and iterated trials of potentially better evaluation plans. The resulting algorithms are not only effective on LCDBs, but also applicable to existing query languages. A number of specific constraint algebra algorithms are also developed: select-project-join for two relations, constraint sort-join and constraint multi-join.     

Reasoning about equations and functional dependencies on complexobjects

Virtually all semantic or object-oriented data models assume that objects have an identity separate from any of their parts, and allow users to define complex object types in which part values may be any other objects. This often results in a choice of query language in which a user can express navigating from one object to another by following a property value path. We consider a constraint language in which one may express equations and functional dependencies over complex object types. The language is novel in the sense that component attributes of individual constraints may correspond to property paths. The kind of equations we consider are also important, because they are a natural abstraction of the class of conjunctive queries for query languages that support property value navigation. In our introductory comments, we give an example of such a query and outline two applications of the constraint theory to problems relating to a choice of access plan for the query. We present a sound and complete axiomatization of the constraint language for the case in which interpretations are permitted to be infinite, where interpretations themselves correspond to a form of directed labeled graph. Although the implication problem for our form of equational constraint alone over arbitrary schema is undecidable, we present decision procedures for the implication problem for both kinds of constraints when the problem schema satisfies a stratification condition, and when all input functional dependencies are keys     

Querying Linguistic Trees

Large databases of linguistic annotations are used for testing linguistic hypotheses and for training language processing models. These linguistic annotations are often syntactic or prosodic in nature, and have a hierarchical structure. Query languages are used to select particular structures of interest, or to project out large slices of a corpus for external analysis. Existing languages suffer from a variety of problems in the areas of expressiveness, efficiency, and naturalness for linguistic query. We describe the domain of linguistic trees and discuss the expressive requirements for a query language. Then we present a language that can express a wide range of queries over these trees, and show that the language is first-order complete over trees.     

基于参考节点嵌入的图可达性查询

针对k步可达性查询算法无法解决带距离约束的图可达性查询问题,提出基于参考节点嵌入的图可达性查询算法。首先,从所有节点中选出极少数有代表性的全局参考节点,预先计算所有节点与全局参考节点之间的最短路径距离;然后,采用最短路径树和范围最小值查询技术求得局部参考节点;接着,利用三角不等式关系得到查询点对距离范围;最后,根据查询条件中的距离值与查询点对距离范围上、下限值的大小关系,可快速得出可达性结论。针对社会关系网络和公路网络数据,将所提算法与Dijkstra算法、K-Reach算法进行实验对比测试。相较于K-Reach算法,其索引建立时间小4个数量级,其索引规模小2个数量级;相较于Dijkstra算法,在公路网络和社会关系网络中,直接得出可达性结论的比例分别为92%和78.6%,其查询时间大大缩短,分别降低了95.5%和92%。实验结果表明：所提算法能够通过使用较小的索引开销,实现在线查询计算复杂度的降低,可很好地解决既适用于有权图又适用于无权图带距离约束的可达性查询问题。     

Extending SPARQL with regular expression patterns (for querying RDF)

RDF is a knowledge representation language dedicated to the annotation of resources within the framework of the semantic web. Among the query languages for RDF, SPARQL allows querying RDF through graph patterns, i.e., RDF graphs involving variables. Other languages, inspired by the work in databases, use regular expressions for searching paths in RDF graphs. Each approach can express queries that are out of reach of the other one. Hence, we aim at combining these two approaches. For that purpose, we define a language, called PRDF (for “Path RDF”) which extends RDF such that the arcs of a graph can be labeled by regular expression patterns. We provide PRDF with a semantics extending that of RDF, and propose a correct and complete algorithm which, by computing a particular graph homomorphism, decides the consequence between an RDF graph and a PRDF graph. We then define the PSPARQL query language, extending SPARQL with PRDF graph patterns and complying with RDF model theoretic semantics. PRDF thus offers both graph patterns and path expressions. We show that this extension does not increase the computational complexity of SPARQL and, based on the proposed algorithm, we have implemented a correct and complete PSPARQL query engine.     

面向不确定图的概率可达查询

图的可达性查询被广泛应用于生物网络、社会网络、本体网络、RDF数据库和XML数据库等.由于对数据操作时引入的噪声和错误使这些图数据具有不确定性,已经有大量的针对不确定RDF和XML数据库的研究.文中使用可能世界语义模型构建不确定图,基于该模型,研究了概率可达查询(PR).处理PR查询是#P完全问题,对此文中首先给出一个基本随机算法,可快速地估算出可达概率,并且该值有很高的精确度.进一步,文中为随机算法引入条件分布(称为"条件随机算法"),采用图的不相交路径集和割集作为条件概率分布,因此改进的随机算法可准确地并且是在多项式时间内处理查询.最后基于真实不确定图数据的大量实验结果验证了文中的设计.     

Memoing Evaluation for Constraint Extensions of Datalog

This paper proposes an efficient method for evaluation of deductive queries over constraint databases. The method is based on a combination of the top-down resolution with memoing and the closed form bottom-up evaluation. In this way the top-down evaluation is guaranteed to terminate for all queries for which the bottom-up evaluation terminates. The main advantage of the proposed method is the direct use of the information present in partially instantiated queries without the need for rewriting of the original program. The evaluation algorithm automatically propagates the necessary constraints during the computation. In addition, the top-down evaluation potentially allows the use of compilation techniques, developed for compilers of logic programming languages, which can make the query evaluation very efficient.     

Comparing the expressiveness of downward fragments of the relation algebra with transitive closure on trees

Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add transitive closure, projections, coprojections, intersection, and difference; this for Boolean queries and path queries on labeled and unlabeled structures. In all cases, we present the complete Hasse diagram. In particular, we establish, for each query language fragment that we study on trees, whether it is closed under difference and intersection.