Read-once functions and query evaluation in probabilistic databases

Abstract

Probabilistic databases hold promise of being a viable means for large-scale uncertainty management, increasingly needed in a number of real world applications domains. However, query evaluation in probabilistic databases remains a computational challenge. Prior work on efficient exact query evaluation in probabilistic databases has largely concentrated on query-centric formulations (e.g., safe plans, hierarchical queries), in that, they only consider characteristics of the query and not the data in the database. It is easy to construct examples where a supposedly hard query run on an appropriate database gives rise to a tractable query evaluation problem. In this paper, we develop efficient query evaluation techniques that leverage characteristics of both the query and the data in the database. We focus on tuple-independent databases where the query evaluation problem is equivalent to computing marginal probabilities of Boolean formulas associated with the result tuples. Query evaluation is easy if the Boolean formulas can be factorized into a form that has every variable appearing at most once (called read-once); this suggests a naive approach that incorporates previously developed Boolean formula factorization algorithms into the query evaluation. We then develop novel, more efficient factorization algorithms that work for a large subclass of queries (specifically, conjunctive queries without self-joins), by exploiting the unique structure of the result tuple Boolean formulas. We empirically demonstrate that our proposed techniques are (1) orders of magnitude faster than generic inference algorithms when used to evaluate general read-once functions, and (2) for the special case of hierarchical queries, they rival the efficiency of prior techniques specifically designed to handle such queries.

Anytime approximation in probabilistic databases

“…The equivalent 1OF of any positive DNF formula, if it exists, can be found in polynomial time [23] and is unique up to commutativity of the binary connectives [44]. The 1OF language is particularly relevant in the context of probabilistic databases, since the formulas annotating the results of tractable conjunctive queries without repeating relation symbols on tuple-independent probabilistic databases admit 1OF equivalents [38,51] and their probability can be computed using relational query plans [11,40].…”

Knowledge Compilation Meets Database Theory: Compiling Queries to Decision Diagrams

“…(S(x, y))): here each symbol R, S, T occurs only once and, since q1 is also inversion-free, it follows that it is in UCQ(RO). Note that the characterization of UCQ(RO) is unrelated to Gurvich's characterization of read-once Boolean expressions [19,16], or to the algorithm for checking read-once-ness in [22]: these results are about the lineage, our result is about the query.…”

Querying and Learning in Probabilistic Databases

“…Motivated by queries whose probability computations entail #P-hard [16,15] instances, the query evaluation problem in PDBs has been studied very intensively [16,15,17,38,42,53,59]. Except for two works [50,51], which we are aware of, each of these approaches aims for computing all answers along with their probabilities.…”

“…Recent works on efficient probability computation in PDBs have addressed this problem mostly from two ends. The first group of approaches have restricted the class of queries, i.e., by focusing on safe query plans [16,14,17], or by considering a specific class of tuple-dependencies, commonly referred to as read-once functions [59]. In particular the second group of approaches allows for applying top-k style pruning methods [51,50,8,25] at the time when the query is processed.…”