Algebraic Query Optimization in Database Systems (Algebraische Anfrageoptimierung in Datenbanksystemen)

The thesis investigates different problem classes in algebraic query optimization. For the problem of computing optimal left-deep processing trees with cross products for chain queries and ASI cost functions we present two efficient algorithms. Although, in practice both algorithms yield identical results we have not been able to prove this. For the case of acyclic query graphs, left-deep processing trees, expensive selection and join predicates and ASI cost functions we describe a polynomial time algorithm which is based on a job sequencing algorithm. The algorithm assumes that the set of expensive selections that can be applied directly to the base relations can be guessed. The cheapest plans can be found within the search space of bushy processing trees with cross products. We prove that the problem is NP-hard in this case. The rest of the thesis deals with the general problem of computing optimal bushy processing trees for arbitrary query graphs and expensive selection and join predicates. For this problem we present three efficient dynamic programming algorithms. Our algorithms can handle different join algorithms, split conjunctive predicates, and exploit structural information from the join graph to speed up computation. The time and space complexities of the algorithms are analyzed carefully and efficient implementations based on bitvector arithmetic are presented