Im Folgenden wird ein Promotionsprojekt zur Implementierung und Optimierung von hybriden Indexstrukturen beschrieben. Die erhöhte Suchperformance wird bei hybriden Indexstrukturen durch einen höheren Aufwand an Vorberechnungen bei Einfügeoperationen erreicht. Dadurch ergibt sich, im Gegensatz zu Ansätzen, welche mehrere Indexstrukturen miteinander verbinden oder getrennte Suchanfragen ausführen eine Effizienz der Reorganisation hybrider Indexstrukturen, die prohibitiv für den Einsatz in den meisten Anwendungen ist. Diese sollen innerhalb des Promotionsprojekts optimiert werden, um eine Einsatzfähigkeit in realistischen Szenarien gewährleisten zu können.

This diploma thesis defines the term indexing and in preamble are discussed known indexing algorithms and difference between indexing static and moving objects. The practical part of this diploma thesis is aimed to designing and implementing of indexing algorithm for open source application MaNGOS with respect to generic design pattern and effectiveness of spatial search queries for selection of the objects given properties in the specified area. At the end I present and discuss reached results.

This work is aimed for proposing acceptable indexing of moving objects. With the enlargement of mobile computing it is needed to manage large sets of spatiotemporal data. We introduce the problem of spatiotemporal data and basic general approaches of indexing these data. Further, we show support of spatial data in Oracle. The movement is typically represented as trajectory in two dimensional space with temporal component in third dimension. The thesis contains experiments performed in database Oracle on artificially generate data.

We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from Duquesne and Le Gall's stable continuum random tree. We call these new trees the alpha-gamma trees. In this thesis, we obtain their splitting rules, dislocation measures both in ranked order and in sized-biased order, and we study their limiting behaviour. We further extend the underlying exchangeable fragmentation processes of such trees into partly exchangeable fragmentation processes by weakening the exchangeability. We obtain the integral representations for the measures associated with partly exchangeable fragmentation processes and subordinator of the tagged fragments. We also embed the trees associated with such processes into continuum random trees and study their limiting behaviour. In the end, we generate a three-parameter family of partly exchangeable trees which contains the family of the alpha-gamma trees and another important two-parameter family based on Poisson-Dirichlet distributions.