Constructing Optimal Bushy Processing Trees for Join Queries is NP-hard

We show that constructing optimal bushy processing trees for join queriesis NP-hard. More specifically, we show that even the construction of optimal bushy trees for computing the cross product for a set of relations is NP-hard

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

Optimal Ordering of Selections and Joins in Acyclic Queries with Expensive Predicates

The generally accepted optimization heuristics of pushing selections down does not yield optimal plans in the presence of expensive predicates. Therefore, several researchers have proposed algorithms for the optimal ordering of expensive joins and selections in a query evaluation plan. All of these algorithms have an exponential run time. For a special case, we propose a polynomial algorithm which -- in one integrated step -- computes the optimal join order and places expensive predicates optimally within the join tree. The special case is characterized by the following statements: 1. only left-deep trees are considered, 2. no cross-products are considered, 3. the cost function has to exhibit the ASI property, and 4. cheap selections are pushed before-hand. 1 Introduction Traditional work on algebraic query optimization has mainly focused on the problem of ordering joins in a query. Restrictions like selections and projections are generally treated by "push-down rules". According to t..

Tempolimits - Bemerkungen zur Organisation der Lernzeit in der Schule

Der Text befasst sich mit dem Zeitdruck, unter den Lernen, Bildung und Erziehung in der Schule geraten sind. Die Ursachen des Wechsels von der chronobiologischen Zeit (Rhythmus) zu einer komprimierten und beschleunigten Zeit (Takt) sowie dessen Auswirkungen auf das Alltagsleben werden analysiert (1). Die negativen Auswirkungen der "Hochgeschwindigkeitskultur" auf die inhaltliche Entkernung des Lernens, den Verlust an Bildung und Verstehen in der Schule werden gekennzeichnet (2). Jugendsoziologische Überlegungen zeigen, dass Schule und Jugend nicht zusammenkommen, weil beide unterschiedliche Zeitlogiken folgen (3). Mit einem Plädoyer für die Verlangsamung des Lernens wird deren Bedeutung für Bildungsprozesse am Beispiel einer anderen Lernzeitorganisation der Schule unterstrichen (4). Drei Forschungsgebiete zeigen unerledigte Aufgaben auf (5)