Rewriting queries using views with access patterns under integrity constraints

We study the problem of rewriting queries using views in the presence of access patterns, integrity constraints, disjunction and negation. We provide asymptotically optimal algorithms for (1) finding minimally containing and (2) maximally contained rewritings respecting the access patterns (which we call executable) and for (3) deciding whether an exact executable rewriting exists. We show that rewriting queries using views in this case reduces (a) to rewriting queries with access patterns and constraints without views and also (b) to rewriting queries using views under constraints without access patterns. We show how to solve (a) directly and how to reduce (b) to rewriting queries under constraints only (semantic optimization). These reductions provide two separate routes to a unified solution for problems 1, 2 and 3 based on an extension of the relational chase theory to queries and constraints with disjunction and negation. We also handle equality and arithmetic comparisons. We also show that in an information integration setting, maximally contained rewritings are given by the certain answers (under the usual semantics) for a set of constraints derived from the binding patterns. That is, except for defining the appropriate constraints, binding patterns do not need special treatment. Finally, we show that if there is an exact executable rewriting, there is an executable rewriting which is a union of conjunctive queries with negation.     

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.     

Selecting and using views to compute aggregate queries

We consider a workload of aggregate queries and investigate the problem of selecting materialized views that (1) provide equivalent rewritings for all the queries, and (2) are optimal, in that the cost of evaluating the query workload is minimized. We consider conjunctive views and rewritings, with or without aggregation; in each rewriting, only one view contributes to computing the aggregated query output. We look at query rewriting using existing views and at view selection. In the query-rewriting problem, we give sufficient and necessary conditions for a rewriting to exist. For view selection, we prove complexity results. Finally, we give algorithms for obtaining rewritings and selecting views.     

Query rewritings using views for XPath queries,framework, and methodologies

Query rewriting using views is a technique that allows a query to be answered efficiently by using pre-computed materialized views. It has many applications, such as data caching, query optimization, schema integration, etc. This issue has been studied extensively for relational databases and, as a result, the technology is maturing. For XML data, however, the work is inadequate. Recently, several frameworks have been proposed for query rewriting using views for XPath queries, with the requirement that a rewriting must be complete. In this paper, we study the problem of query rewriting using views for XPath queries without requiring that the rewriting be complete. This will increase its applicability since in many cases, complete rewritings using views do not exist. We give formal definitions for various concepts to formulate the problem, and then propose solutions. Our solutions are built under the framework for query containment. We look into the problem from both theoretic perspectives, and algorithmic approaches. Two methods to generate rewritings using views are proposed, with different characteristics in terms of generalities and efficiencies. The maximality properties of the rewritings generated by these methods are discussed.     

Least common container of tree pattern queries and its applications

Tree patterns represent important fragments of XPath. In this paper, we show that some classes \({\mathcal{C}}\) of tree patterns exhibit such a property that, given a finite number of compatible tree patterns \({P_1, \ldots, P_n\in \mathcal{C}}\), there exists another pattern P such that P ₁, . . . , P _n are all contained in P, and for any tree pattern \({Q\in \mathcal{C}}\), P ₁, . . . , P _n are all contained in Q if and only if P is contained in Q. We experimentally demonstrate that the pattern P is usually much smaller than P ₁, . . . , P _n combined together. Using the existence of P above, we show that testing whether a tree pattern, P, is contained in another, \({Q\in \mathcal{C}}\), under an acyclic schema graph G, can be reduced to testing whether P _G , a transformed version of P, is contained in Q without any schema graph, provided that the distinguished node of P is not labeled *. We then show that, under G, the maximal contained rewriting (MCR) of a tree pattern Q using a view V can be found by finding the MCR of Q using V _G without G, when there are no *-nodes on the distinguished path of V and no *-nodes in Q.     

Using views to generate efficient evaluation plans for queries

We study the problem of generating efficient, equivalent rewritings using views to compute the answer to a query. We take the closed-world assumption, in which views are materialized from base relations, rather than views describing sources in terms of abstract predicates, as is common when the open-world assumption is used. In the closed-world model, there can be an infinite number of different rewritings that compute the same answer, yet have quite different performance. Query optimizers take a logical plan (a rewriting of the query) as an input, and generate efficient physical plans to compute the answer. Thus our goal is to generate a small subset of the possible logical plans without missing an optimal physical plan.We first consider a cost model that counts the number of subgoals in a physical plan, and show a search space that is guaranteed to include an optimal rewriting, if the query has a rewriting in terms of the views. We also develop an efficient algorithm for finding rewritings with the minimum number of subgoals. We then consider a cost model that counts the sizes of intermediate relations of a physical plan, without dropping any attributes, and give a search space for finding optimal rewritings. Our final cost model allows attributes to be dropped in intermediate relations. We show that, by careful variable renaming, it is possible to do better than the standard “supplementary relation” approach, by dropping attributes that the latter approach would retain. Experiments show that our algorithm of generating optimal rewritings has good efficiency and scalability.     

Ontology evolution without tears

The evolution of ontologies is an undisputed necessity in ontology-based data integration. Yet, few research efforts have focused on addressing the need to reflect the evolution of ontologies used as global schemata onto the underlying data integration systems. In most of these approaches, when ontologies change their relations with the data sources, i.e., the mappings, are recreated manually, a process which is known to be error-prone and time-consuming. In this paper, we provide a solution that allows query answering in data integration systems under evolving ontologies without mapping redefinition. This is achieved by rewriting queries among ontology versions and then forwarding them to the underlying data integration systems to be answered. To this purpose, initially, we automatically detect and describe the changes among ontology versions using a high level language of changes. Those changes are interpreted as sound global-as-view (GAV) mappings, and they are used in order to produce equivalent rewritings among ontology versions. Whenever equivalent rewritings cannot be produced we a) guide query redefinition or b) provide the best “over-approximations”, i.e., the minimally-containing and minimally-generalized rewritings. We prove that our approach imposes only a small overhead over traditional query rewriting algorithms and it is modular and scalable. Finally, we show that it can greatly reduce human effort spent since continuous mapping redefinition is no longer necessary.     

Rewriting Union Queries Using Views

The problem of finding contained rewritings of queries using views is of great importance in mediated data integration systems. In this paper, we first present a general approach for finding contained rewritings of unions of conjunctive queries with arbitrary built-in predicates. Our approach is based on an improved method for testing conjunctive query containment in this context. Although conceptually simple, our approach generalizes previous methods for finding contained rewritings of conjunctive queries and is more powerful in the sense that many rewritings that can not be found using existing methods can be found by our approach. Furthermore, implication constraints (Zhang, X., & Ozsoyoglu, Z.M. (1997). Implication and referential constraints: A new formal resaoning. IEEE TKDE, 9(6):894–910, Now/Dec.) over the base relations can be easily handled. We then present a simplified approach which is less complete, but is much faster than the general approach, and it still finds maximum rewritings in several special cases. Our general approach finds more rewritings than previous algorithms such as the Bucket and the resolution-based algorithms. Our simplified approach generalizes the U-join and the MiniCon algorithms with no loss of efficiency.     

Query rewriting using views in the presence of functional and inclusion dependencies

Query rewriting using views is a technique for determining how a query may be answered using a given set of resources, which may include materialized views, cached results of previous queries, or queries answerable by other databases. The power of query rewriting can be considerably enhanced by taking into account integrity constraints that are known to hold on base relations. This paper describes an extension of query rewriting that utilizes inclusion dependencies to find rewritings of queries that would otherwise be overlooked. We describe a complete strategy for finding rewritings in the presence of inclusion dependencies and present a basic algorithm that implements that strategy. We also describe extensions to this algorithm when both inclusion and functional dependencies are considered.     

一种基于可排序视图的RDF模式匹配算法

随着语义网络中数据量的激增,在RDF数据集中高效查询数据已成为一个亟待解决的问题。传统的基于物化视图的RDF模式匹配方法虽然能降低表的自连接操作次数,加快查询模式重写过程,但在视图集中检索模式匹配的视图等价于子图同构这一NP-hard问题。为了减小查询模式重写代价,提高RDF模式匹配过程效率,引入可排序视图概念,设计包含映射发现算法contain及其扩展算法contain+,简化等长度模式间包含映射发现过程,同时保证模式间的匹配代价与输入数据的规模线性相关。此外,提出基于倒排表/MapReduce检索候选可排序视图的方法,实现RDF模式重写算法rewrite,用以处理不同规模数据集上的模式匹配问题。理论分析及实验证明,基于可排序视图的RDF模式匹配算法能有效地兼顾算法效率及算法可扩展性。     

Efficient evaluation of query rewriting plan over materialized XML view

The query rewriting plan generation over XML views has received wide attention recently. However, little work has been done on efficient evaluation of the query rewriting plans, which is not trivial since the plan may contain an exponential size of sub-plans. This paper investigates the reason for the potentially exponential number of sub-plans, and then proposes a new space-efficient form called ABCPlan (Plan with Automata Based Combinations) to equivalently represent the original query rewriting plan. ABCPlan contains a set of buckets containing suffix paths in the query tree and an automata to indicate the combination of the suffix paths from different buckets as valid query rewriting sub-plans. We also design an evaluation method called ABCScan, which constructs a unified evaluation tree for the ABCPlan and handles the evaluation tree in one scan of the XML view. In the evaluation, we introduce node existence automata to encode the structure of the sub-tree and convert the satisfaction of the ABCPlan into the intersection problem of deterministic finite automata. The experiments show that ABCPlan based method outperforms existing methods significantly in terms of scalability and efficiency.     

A note on a special one-rule semi-Thue system

We show that the special semi-Thue system S₁ = {(abba, λ)} has no equivalent finite semi-Thue system which is uniquely terminating, i.e. canonical. This gives another example of a Thue system with a decidable word problem, but solving it using a canonical string rewriting system is possible only by introducing new additional symbols. In contrast to the example obtained recently by Kapur and Narendran (1984) this system presents a monoid which is in fact a group.     

View-based query processing: On the relationship between rewriting,answering and losslessness

As a result of the extensive research in view-based query processing, three notions have been identified as fundamental, namely rewriting, answering, and losslessness. Answering amounts to computing the tuples satisfying the query in all databases consistent with the views. Rewriting consists in first reformulating the query in terms of the views and then evaluating the rewriting over the view extensions. Losslessness holds if we can answer the query by solely relying on the content of the views. While the mutual relationship between these three notions is easy to identify in the case of conjunctive queries, the terrain of notions gets considerably more complicated going beyond such a query class. In this paper, we revisit the notions of answering, rewriting, and losslessness and clarify their relationship in the setting of semistructured databases, and in particular for the basic query class in this setting, i.e., two-way regular path queries. Our first result is a clean explanation of the relationship between answering and rewriting, in which we characterize rewriting as a “linear approximation” of query answering. We show that applying this linear approximation to the constraint-satisfaction framework yields an elegant automata-theoretic approach to query rewriting. As for losslessness, we show that there are indeed two distinct interpretations for this notion, namely with respect to answering, and with respect to rewriting. We also show that the constraint-theoretic approach and the automata-theoretic approach can be combined to give algorithmic characterization of the various facets of losslessness. Finally, we deal with the problem of coping with loss, by considering mechanisms aimed at explaining lossiness to the user.     

A REVIEW OF TREE CONVEX SETS TEST

A collection of sets may have some interesting properties which help identify efficient algorithms for constraint satisfaction problems and combinatorial auction problems. One of the properties is tree convexity. A collection S of sets is tree convex if we can find a tree T whose nodes are the union of the sets of S and each set of S is the nodes of a subtree of T . This concept extends that of row convex sets each of which is an interval over a total ordering of the elements of the union of these sets. An interesting problem is to find efficient algorithms to test whether a collection of sets is tree convex. It is not known before if there exists a linear time algorithm for this test. In this paper, we review the materials that are the key to a linear algorithm: hypergraphs, a characterization of tree convex sets and the acyclic hypergraph test algorithm. Some typos in the original paper of the acyclicity test are corrected here. Some experiments show that the linear algorithm is significantly faster than a well‐known existing algorithm.     

Exact and approximate rhythm matching algorithms

An interesting problem in music information retrieval is to classify songs according to rhythms. A rhythm is represented by a sequence of “Quick” (Q) and “Slow” (S) symbols, which correspond to the (relative) duration of notes, such that S?=?2Q. Christodoulakis et?al. presented an efficient algorithm that can be used to classify musical sequences according to rhythms. In this article, the above algorithm is implemented, along with a naive brute force algorithm to solve the same problem. The theoretical time complexity bounds are analyzed with the actual running times achieved by the experiments, and the results of the two algorithms are compared. Furthermore, new efficient algorithms are presented that take temporal errors into account. This, the approximate pattern matching version, could not be handled by the algorithms previously presented. The running times of two algorithmic variants are analyzed and compared and examples of their implementation are shown.     

Descendants of a recognizable tree language for sets of linear monadic term rewrite rules

For a tree language L and a set S of term rewrite rules over Σ, the descendant of L for S is the set S^∗(L) of trees reachable from a tree in L by rewriting in S. For a recognizable tree language L, we study the set D(L) of descendants of L for all sets of linear monadic term rewrite rules over Σ. We show that D(L) is finite. For each tree automaton A over Σ, we can effectively construct a set {R₁,…,Rk} of linear monadic term rewrite systems over Σ such that and for any 1?i<j?k, .     

From Chemical Rules to Term Rewriting

In this paper, rule-based programming is explored in the field of automated generation of chemical reaction mechanisms. We explore a class of graphs and a graph rewriting relation where vertices are preserved and only edges are changed. We show how to represent cyclic labeled graphs by decorated labeled trees or forests, then how to transform trees into terms. A graph rewriting relation is defined, then simulated by a tree rewriting relation, which can be in turn simulated by a rewriting relation on equivalence classes of terms. As a consequence, this kind of graph rewriting can be implemented using term rewriting. This study is motivated by the design of the GasEl system for the generation of kinetics reactions mechanisms. In GasEl, chemical reactions correspond to graph rewrite rules and are implemented by conditional rewriting rules in ELAN. The control of their application is done through the ELAN strategy language.     

Widening techniques for regular tree model checking

We consider the framework of regular tree model checking where sets of configurations of a system are represented by regular tree languages and its dynamics is modeled by a term rewriting system (or a regular tree transducer). We focus on the computation of the reachability set R*(L) where R is a regular tree transducer and L is a regular tree language. The construction of this set is not possible in general. Therefore, we present a general acceleration technique, called regular tree widening which allows to speed up the convergence of iterative fixpoint computations in regular tree model checking. This technique can be applied uniformly to various kinds of transformations. We show the application of our framework to different analysis contexts: verification of parameterized tree networks and data-flow analysis of multithreaded programs. Parametrized networks are modeled by relabeling tree transducers, and multithreaded programs are modeled by term rewriting rules encoding transformations on control structures. We prove that our widening technique can emulate many existing algorithms for special classes of transformations and we show that it can deal with transformations beyond the scope of these algorithms.