Algorithms with theoretical guarantees for several database problems

In this thesis, we propose data structures and/or algorithms with theoretical guarantees for solving a series of problems that find applications in database systems. These problems can be classified into two categories. The first one contains several classic problems in computer science, including the approximate nearest neighbor problem, the approximate closest pair problem, the skyline problem (a.k.a. the maxima problem), and 2d orthogonal range search. The second category, on the other hand, consists of problems that are newly introduced by this thesis: the historical quantile problem , the k-skip shortest path problem, the nearest keyword problem on XML documents, the most connected vertex problem, and the FIFO indexing problem. For each problem, we establish either the worst-case efficiency of our solutions, or their instance optimality when worst-case performance is not interesting.