Exploiting non-uniform query distributions in data structuring problems

This thesis examines data structures with query times that are a function of the distribution of queries made to them. When a query distribution exhibits nonuniformity—as is often the case in many applications—the sequence of queries can often be executed faster: Several such problems are considered. For the dictionary problem, this thesis presents the first binary search tree to achieve the working-set property for individual queries in the worst case, a data structure that supports searching from arbitrary temporal fingers, and a data structure that supports a stronger version of the unified property. For the predecessor search problem in bounded universes, this thesis presents a data structure that answers queries in time that is a function of the distance between the query and its answers (which leads to several appli¢ations in the areas of nearest neighbour search and range searching), as well as several data structures that answer queries in time that is a function of the entropy of the query distribution and various space requirements.