Ralf Rantzau

Context-sensitive ranking

Contextual preferences take the form that item i1 is preferred to item i2 in the context of X. For example, a preference might state the choice for Nicole Kidman over Penelope Cruz in drama movies, whereas another preference might choose Penelope Cruz over Nicole Kidman in the context of Spanish dramas. Various sources provide preferences independently and thus preferences may contain cycles and contradictions. We reconcile democratically the preferences accumulated from various sources and use them to create a priori orderings of tuples in an off-line preprocessing step. Only a few representative orders are saved, each corre-sponding to a set of contexts. These orders and associated contexts are used at query time to expeditiously provide ranked answers. We formally define contextual preferences, provide algorithms for creating orders and processing queries, and present experimental results that show their efficacy and practical utility.

Laws for Rewriting Queries Containing Division Operators

Relational division, also known as small divide, is derived operator of the relational algebra that realizes many-to-one set containment test, where a set is represented as a group of tuples: Small divide discovers which sets in a dividend relation contain all elements of the set stored in a divisor relation. The great divide operator extends small divide by realizing many-to-many set containment tests. It is also similar to the set containment join operator for schemas that are not in first normal form. Neither small nor great divide has been implemented in commercial relational database systems although the operators solve important problems and many efficient algorithms for them exist. We present algebraic laws that allow rewriting expressions containing small or great divide, illustrate their importance for query optimization, and discuss the use of great divide for frequent itemset discovery, an important data mining primitive. A recent theoretic result shows that small divide must be implemented by special purpose algorithms and not be simulated by pure relational algebra expressions to achieve efficiency. Consequently, an efficient implementation requires that the optimizer treats small divide as a first-class operator and possesses powerful algebraic laws for query rewriting.