Combining incompleteness and ranking in tree queries

In many cases, users may want to consider incomplete answers to their queries. Often, however, there is an overwhelming number of such answers, even if subsumed answers are ignored and only maximal ones are considered. Therefore, it is important to rank answers according to their degree of incompleteness and, moreover, this ranking should be combined with other, conventional ranking techniques that are already in use (e.g., the relevance of answers to keywords). Query evaluation should take the ranking into account by computing answers incrementally, i.e., in ranked order. In particular, the evaluation process should generate the top-k answers efficiently. We show how a semantics for incomplete answers to tree queries can be combined with common ranking techniques. In our approach, answers are rewarded for relevancy and penalized for incompleteness, where the user specifies the appropriate quantum. An incremental algorithm for evaluating tree queries is given. This algorithm enumerates in ranked order with polynomial delay, under query-and-data complexity. Our results are couched in terms of a formal framework that captures a variety of data models (e.g., relational, semistructured and XML).