Extracting minimum-weight tree patterns from a schema with neighborhood constraints

The task of formulating queries is greatly facilitated when they can be generated automatically from some given data values, schema concepts or both (e.g., names of particular entities and XML tags). This automation is the basis of various database applications, such as keyword search and interactive query formulation. Usually, automatic query generation is realized by finding a set of small tree patterns that contain some given labels. More formally, the computational problem at hand is to find top-k patterns, that is, k minimumweight tree patterns that contain a given bag of labels, conform to the schema, and are non-redundant. A plethora of systems and research papers include a component that deals with this problem. This paper presents an algorithm for this problem, with complexity guarantees, that allows nontrivial schema constraints and, hence, avoids generating patterns that cannot be instantiated. Specifically, this paper shows that for schemas with certain types of neighborhood constraints, the problem is fixed-parameter tractable (FPT), the parameter being the size of the given bag of labels. As machinery, an adaptation of Lawler-Murty's procedure is developed. This adaptation reduces a top-k problem, over an infinite space of solutions, to a prefix-constrained optimization problem. It is shown how to cast the problem of top-k patterns in this adaptation. A solution is developed for the corresponding prefix-constrained optimization problem, and it uses an algorithm for finding a (single) minimum-weight tree pattern. This algorithm generalizes an earlier work by handling leaf constraints (i.e., which labels may, must or should not be leaves). It all boils down to a reduction showing that, under a language for neighborhood constraints, finding top-k patterns is FPT if a certain variant of exact cover is FPT.