Benny Kimelfeld

Finding and approximating top-k answers in keyword proximity search

Various approaches for keyword proximity search have been implemented in relational databases, XML and the Web. Yet, in all of them, an answer is a Q-fragment, namely, a subtree T of the given data graph G, such that T contains all the keywords of the query Q and has no proper subtree with this property. The rank of an answer is inversely proportional to its weight. Three problems are of interest: finding an optimal (i.e., top-ranked) answer, computing the top-k answers and enumerating all the answers in ranked order. It is shown that, under data complexity, an efficient algorithm for solving the first problem is sufficient for solving the other two problems with polynomial delay. Similarly, an efficient algorithm for finding a θ-approximation of the optimal answer suffices for carrying out the following two tasks with polynomial delay, under query-and-data complexity. First, enumerating in a (θ+1)-approximate order. Second, computing a (θ+1)-approximation of the top-k answers. As a corollary, this paper gives the first efficient algorithms, under data complexity, for enumerating all the answers in ranked order and for computing the top-k answers. It also gives the first efficient algorithms, under query-and-data complexity, for enumerating in a provably approximate order and for computing an approximation of the top-k answers.

Keyword proximity search in complex data graphs

In keyword search over data graphs, an answer is a nonredundant subtree that includes the given keywords. An algorithm for enumerating answers is presented within an architecture that has two main components: an engine that generates a set of candidate answers and a ranker that evaluates their score. To be effective, the engine must have three fundamental properties. It should not miss relevant answers, has to be efficient and must generate the answers in an order that is highly correlated with the desired ranking. It is shown that none of the existing systems has implemented an engine that has all of these properties. In contrast, this paper presents an engine that generates all the answers with provable guarantees. Experiments show that the engine performs well in practice. It is also shown how to adapt this engine to queries under the OR semantics. In addition, this paper presents a novel approach for implementing rankers destined for eliminating redundancy. Essentially, an answer is ranked according to its individual properties (relevancy) and its intersection with the answers that have already been presented to the user. Within this approach, experiments with specific rankers are described.

Query efficiency in probabilistic XML models

Various known models of probabilistic XML can be represented as instantiations of abstract p-documents. Such documents have, in addition to ordinary nodes, distributional nodes that specify the probabilistic process of generating a random document. Within this abstraction, families of pdocuments, which are natural extensions and combinations of previous models, are considered. The focus is on efficiency of applying twig queries (with projection) to p-documents. A closely related issue is the ability to (efficiently) translate a given document of one family into another family. Furthermore, both of these tasks have two variants that correspond to the value-based and object-based semantics. The translation relationships among different families of p-documents are studied. An efficient algorithm for evaluating twig queries over one specific family is given. This algorithm generalizes a known algorithm and significantly improves its running time, both analytically and experimentally. It is shown that this family is the maximal, among the ones considered, for which query evaluation is tractable. For the rest, efficient approximate algorithms for query evaluation are presented.

On the expressiveness of probabilistic XML models

Various known models of probabilistic XML can be represented as instantiations of the abstract notion of p-documents. In addition to ordinary nodes, p-documents have distributional nodes that specify the possible worlds and their probabilistic distribution. Particular families of p-documents are determined by the types of distributional nodes that can be used as well as by the structural constraints on the placement of those nodes in a p-document. Some of the resulting families provide natural extensions and combinations of previously studied probabilistic XML models. The focus of the paper is on the expressive power of families of p-documents. In particular, two main issues are studied. The first is the ability to (efficiently) translate a given p-document of one family into another family. The second is closure under updates, namely, the ability to (efficiently) represent the result of updating the instances of a p-document of a given family as another p-document of that family. For both issues, we distinguish two variants corresponding to value-based and object-based semantics of p-documents.

Interconnection semantics for keyword search in XML

A framework for describing semantic relationships among nodes in XML documents is presented. In contrast to earlier work, the XML documents may have ID references (i.e., they correspond to graphs and not just trees). A specific interconnection semantics in this framework can be defined explicitly or derived automatically. The main advantage of interconnection semantics is the ability to pose queries on XML data in the style of keyword search. Several methods for automatically deriving interconnection semantics are presented. The complexity of the evaluation and the satisfiability problems under the derived semantics is analyzed. For many important cases, the complexity is tractable and hence, the proposed interconnection semantics can be efficiently applied to real-world XML documents.

Query evaluation over probabilistic XML

Query evaluation over probabilistic XML is explored. The queries are twig patterns with projection, and the data is represented in terms of three models of probabilistic XML (that extend existing ones in the literature). The first model makes an assumption of independence among the probabilistic junctions, whereas the second model can encode probabilistic dependencies. The third model combines the first two and, hence, is the most general. An efficient algorithm (under data complexity) is given for query evaluation in the first model. In addition, various optimizations are proposed, and their effectiveness is shown both analytically and experimentally. For the other two models, it is shown that every query is either intractable or trivial. Nonetheless, efficient (additive and multiplicative) approximation algorithms are given for these two models. Finally, Boolean queries are enriched by allowing disjunctions and negations of branches. The above algorithm for the first model is extended to handle these queries. For the other two models, there is an efficient additive approximation, and a multiplicative one also exists if there is no negation; in addition, it is shown that if the query is non-monotonic, then no efficient multiplicative approximation exists unless NP = RP.

Running tree automata on probabilistic XML

Tree automata (specifically, bottom-up and unranked) form a powerful tool for querying and maintaining validity of XML documents. XML with uncertain data can be modeled as a probability space of labeled trees, and that space is often represented by a tree with distributional nodes. This paper investigates the problem of evaluating a tree automaton over such a representation, where the goal is to compute the probability that the automaton accepts a random possible world. This problem is generally intractable, but for the case where the tree automaton is deterministic (and its transitions are defined by deterministic string automata), an efficient algorithm is presented. The paper discusses the applications of this result, including the ability to sample and to evaluate queries (e.g., in monadic second-order logic) while requiring a-priori conformance to a schema (e.g., DTD). XML schemas also include attribute constraints, and the complexity of key, foreign-key and inclusion constraints are studied in the context of probabilistic XML. Finally, the paper discusses the generalization of the results to an extended data model, where distributional nodes can repeatedly sample the same subtree, thereby adding another exponent to the size of the probability space.

Probabilistic XML: Models and Complexity

Uncertainty in data naturally arises in various applications, such as data integration and Web information extraction. Probabilistic XML is one of the concepts that have been proposed to model and manage various kinds of uncertain data. In essence, a probabilistic XML document is a compact representation of a probability distribution over ordinary XML documents. Various models of probabilistic XML provide different languages, with various degrees of expressiveness, for such compact representations. Beyond representation, probabilistic XML systems are expected to support data management in a way that properly reflects the uncertainty. For instance, query evaluation entails probabilistic inference, and update operations need to properly change the entire probability space. Efficiently and effectively accomplishing data-management tasks in that manner is a major technical challenge. This chapter reviews the literature on probabilistic XML. Specifically, this chapter discusses the probabilistic XML models that have been proposed, and the complexity of query evaluation therein. Also discussed are other data-management tasks like updates and compression, as well as systemic and implementation aspects.

Revisiting redundancy and minimization in an XPath fragment

Redundancy and minimization of queries are investigated in a well known fragment of XPath that includes child and descendant edges, branches, wildcards, and multiple output nodes. Contrary to a published result, a proposed technique does not guarantee minimality or even non-redundancy, and it is unknown whether a non-redundant query is also minimal. It is shown that for two sub-fragments, non-redundancy and minimality are the same, and can be realized by means of simple (local) tests. The latter property is used to prove that testing non-redundancy is NP-complete.

A dichotomy in the complexity of deletion propagation with functional dependencies

A classical variant of the view-update problem is deletion propagation, where tuples from the database are deleted in order to realize a desired deletion of a tuple from the view. This operation may cause a (sometimes necessary) side effect---deletion of additional tuples from the view, besides the intentionally deleted one. The goal is to propagate deletion so as to maximize the number of tuples that remain in the view. In this paper, a view is defined by a self-join-free conjunctive query (sjf-CQ) over a schema with functional dependencies. A condition is formulated on the schema and view definition at hand, and the following dichotomy in complexity is established. If the condition is met, then deletion propagation is solvable in polynomial time by an extremely simple algorithm (very similar to the one observed by Buneman et al.). If the condition is violated, then the problem is NP-hard, and it is even hard to realize an approximation ratio that is better than some constant; moreover, deciding whether there is a side-effect-free solution is NP-complete. This result generalizes a recent result by Kimelfeld et al., who ignore functional dependencies. For the class of sjf-CQs, it also generalizes a result by Cong et al., stating that deletion propagation is in polynomial time if keys are preserved by the view.