Tree patterns form a natural basis to query tree-structured data such as XML and LDAP. Since the efficiency of tree pattern matching against a tree-structured database depends on the size of the pattern, it is essential to identify and eliminate redundant nodes in the pattern and do so as quickly as possible. In this paper, we study tree pattern minimization both in the absence and in the presence of integrity constraints (ICs) on the underlying tree-structured database. When no ICs are considered, we call the process of minimizing a tree pattern, constraint-independent minimization. We develop a polynomial time algorithm called CIM for this purpose. CIM's efficiency stems from two key properties: (i) a node cannot be redundant unless its children are, and (ii) the order of elimination of redundant nodes is immaterial. When ICs are considered for minimization, we refer to it as constraint-dependent minimization. For treestructured databases, required child/descendant and type co-occurrence ICs are very natural. Under such ICs, we show that the minimal equivalent query is unique. We show the surprising result that the algorithm obtained by first augmenting the tree pattern using ICs, and then applying CIM, always finds the unique minimal equivalent query; we refer to this algorithm as ACIM. While ACIM is also polynomial time, it can be expensive in practice because of its inherent non-locality. We then present a fast algorithm, CDM, that identifies and eliminates local redundancies due to ICs, based on propagating "information labels" up the tree pattern. CDM can be applied prior to ACIM for improving the minimization efficiency. We complement our analytical results with an experimental study that shows the effectiveness of our tree pattern minimization techniques. 1.

Abstract not found

U.C. San Diego

We study the complexity and expressive power of conjunctive queries over unranked labeled trees, where the tree structures are represented using "axis relations" such as "child", "descendant", and "following" (we consider a superset of the XPath axes) as well as unary relations for node labels. (Cyclic) conjunctive queries over trees occur in a wide range of data management scenarios related to XML, the Web, and computational linguistics. We establish a framework for characterizing structures representing trees for which conjunctive queries can be evaluated e#- ciently. Then we completely chart the tractability frontier of the problem for our axis relations, i.e., we find all subsetmaximal sets of axes for which query evaluation is in polynomial time. All polynomial-time results are obtained immediately using the proof techniques from our framework. Finally, we study the expressiveness of conjunctive queries over trees and compare it to the expressive power of fragments of XPath. We show that for each conjunctive query, there is an equivalent acyclic positive query (i.e., a set of acyclic conjunctive queries), but that in general this query is not of polynomial size.

View-based query processing requires to answer a query posed to a database only on the basis of the information on a set of views, which are again queries over the same database. This problem is relevant in many aspects of database management, and has been addressed by means of two basic approaches, namely, query rewriting and query answering. In the former approach, one tries to compute a rewriting of the query in terms of the views, whereas in the latter, one aims at directly answering the query based on the view extensions. We study view-based query processing for the case of regular-path queries, which are the basic querying mechanisms for the emergent field of semistructured data. Based on recent results, we first show that a rewriting is in general a co-NP function wrt to the size of view extensions. Hence, the problem arises of characterizing which instances of the problem admit a rewriting that is PTIME. A second contribution of the work is to establish a tight connection between view-based query answering and constraint-satisfaction problems, which allows us to show that the above characterization is going to be difficult. As a third contribution of our work, we present two methods for computing PTIME rewritings of specific forms. The first method, which is based on the established connection with constraint-satisfaction problems, gives us rewritings expressed in Datalog with a fixed number of variables. The second method, based on automata-theoretic techniques, gives us rewritings that are formulated as unions of conjunctive regular-path queries with a fixed number of variables.

Securing access to data in location-based services and mobile applications requires the definition of spatially aware access control systems. Even if some approaches have already been proposed either in the context of geographic database systems or context-aware applications, a comprehensive framework, general and flexible enough to cope with spatial aspects in real mobile applications, is still missing. In this paper, we make one step towards this direction and we present GEO-RBAC, an extension of the RBAC model to deal with spatial and location-based information. In GEO-RBAC, spatial entities are used to model objects, user positions, and geographically bounded roles. Roles are activated based on the position of the user. Besides a physical position, obtained from a given mobile terminal or a cellular phone, users are also assigned a logical and device independent position, representing the feature (the road, the town, the region) in which they are located. To make the model more flexible and re-usable, we also introduce the concept of role schema, specifying the name of the role as well as the type of the role spatial boundary and the granularity of the logical position. We then extend GEO-RBAC to cope with hierarchies, modeling permission, user, and activation inheritance, and separation of duty constraints. The proposed classes of constraints extend traditional ones to deal with different granularities (schema/instance

We systematically investigate the connections between constraint satisfaction problems, structures of bounded treewidth, and definability in logics with a finite number of variables. We first show that constraint satisfaction problems on inputs of treewidth less than k are definable using Datalog programs with at most k variables; this provides a new explanation for the tractability of these classes of problems. After this, we investigate constraint satisfaction on inputs that are homomorphically equivalent to structures of bounded treewidth.

XML queries are usually expressed by means of XPath expressions identifying portions of the selected documents. An XPath expression defines a way of navigating an XML tree and returns the set of nodes which are reachable from one or more starting nodes through the paths specified by the expression. The problem of efficiently answering XPath queries is very interesting and has recently received increasing attention by the research community. In particular, an increasing effort has been devoted to define effective optimization techniques for XPath queries. One of the main issues related to the optimization of XPath queries is their minimization. The minimization of XPath queries has been studied for limited fragments of XPath, containing only the descendent, the child and the branch operators. In this work, we address the problem of minimizing XPath queries for a more general fragment, containing also the wildcard operator. We characterize the complexity of the minimization of XPath queries, stating that it is NP-hard, and propose an algorithm for computing minimum XPath queries. Moreover, we identify an interesting tractable case and propose an ad hoc algorithm handling the minimization of this kind of queries in polynomial time.

When data sources are virtually integrated there is no common and centralized mechanism for maintaining global consistency. In consequHHj9 it is likely that inconsistencies with respect to certain global integrity constraints (ICs)will occu; In this chapter we consider the problem of defining andcompu2;) those answers that are consistent wrt the global ICs when global qubal) are posed tovirtuM data integration systems whosesou)33 are specified following the local-as-view approach.

We provide a characterization of the resolution width introduced in the context of propositional proof complexity in terms of the existential pebble game introduced in the context of finite model theory. The characterization is tight and purely combinatorial. Our first application of this result is a surprising proof that the minimum space of refuting a 3-CNF formula is always bounded from below by the minimum width of refuting it (minus 3). This solves a well-known open problem. The second application is the unification of several width lower bound arguments, and a new width lower bound for the Dense Linear Order Principle. Since we also show that this principle has resolution refutations of polynomial size, this provides yet another example showing that the size-width relationship is tight.