Approximation and relaxation of semantic web path queries

Given the heterogeneity of complex graph data on the web, such as RDF linked data, it is likely that a user wishing to query such data will lack full knowledge of the structure of the data and of its irregularities. Hence, providing flexible querying capabilities that assist users in formulating their information seeking requirements is highly desirable. In this paper we undertake a detailed theoretical investigation of query approximation, query relaxation, and their combination, for this purpose. The query language we adopt comprises conjunctions of regular path queries, thus encompassing recent extensions to SPARQL to allow for querying paths in graphs using regular expressions (SPARQL 1.1). To this language we add standard notions of query approximation based on edit distance, as well as query relaxation based on RDFS inference rules. We show how both of these notions can be integrated into a single theoretical framework and we provide incremental evaluation algorithms that run in polynomial time in the size of the query and the data, returning answers in ranked order of their `distance' from the original query. We also combine for the first time these two disparate notions into a single `flex' operation that simultaneously applies both approximation and relaxation to a query conjunct, providing even greater flexibility for users, but still retaining polynomial time evaluation complexity and the ability to return query answers in ranked order