Dokument

Summary:
Nahezu alle naturwissenschaftlichen Bereiche profitieren von neuesten Analyse- und Verarbeitungsmethoden für große Datenmengen. Diese Verfahren setzten eine effiziente Verarbeitung von geo- und zeitbezogenen Daten voraus, da die Zeit und die Position wichtige Attribute vieler Daten sind. Die effiziente Anfrageverarbeitung wird insbesondere durch den Einsatz von Indexstrukturen ermöglicht. Im Fokus dieser Arbeit liegen zwei Indexstrukturen: Multiversion B-Baum (MVBT) und R-Baum. Die erste Struktur wird für die Verwaltung von zeitbehafteten Daten, die zweite für die Indexierung von mehrdimensionalen Rechteckdaten eingesetzt. Ständig- und schnellwachsendes Datenvolumen stellt eine große Herausforderung an die Informatik dar. Der Aufbau und das Aktualisieren von Indexen mit herkömmlichen Methoden (Datensatz für Datensatz) ist nicht mehr effizient. Um zeitnahe und kosteneffiziente Datenverarbeitung zu ermöglichen, werden Verfahren zum schnellen Laden von Indexstrukturen dringend benötigt. Im ersten Teil der Arbeit widmen wir uns der Frage, ob es ein Verfahren für das Laden von MVBT existiert, das die gleiche I/O-Komplexität wie das externe Sortieren besitz. Bis jetzt blieb diese Frage unbeantwortet. In dieser Arbeit haben wir eine neue Kostruktionsmethode entwickelt und haben gezeigt, dass diese gleiche Zeitkomplexität wie das externe Sortieren besitzt. Dabei haben wir zwei algorithmische Techniken eingesetzt: Gewichts-Balancierung und Puffer-Bäume. Unsere Experimenten zeigen, dass das Resultat nicht nur theoretischer Bedeutung ist. Im zweiten Teil der Arbeit beschäftigen wir uns mit der Frage, ob und wie statistische Informationen über Geo-Anfragen ausgenutzt werden können, um die Anfrageperformanz von R-Bäumen zu verbessern. Unsere neue Methode verwendet Informationen wie Seitenverhältnis und Seitenlängen eines repräsentativen Anfragerechtecks, um einen guten R-Baum bezüglich eines häufig eingesetzten Kostenmodells aufzubauen. Falls diese Informationen nicht verfügbar sind, optimieren wir R-Bäume bezüglich der Summe der Volumina von minimal umgebenden Rechtecken der Blattknoten. Da das Problem des Aufbaus von optimalen R-Bäumen bezüglich dieses Kostenmaßes NP-hart ist, führen wir zunächst das Problem auf ein eindimensionales Partitionierungsproblem zurück, indem wir die Daten bezüglich optimierte raumfüllende Kurven sortieren. Dann lösen wir dieses Problem durch Einsatz vom dynamischen Programmieren. Die I/O-Komplexität des Verfahrens ist gleich der von externem Sortieren, da die I/O-Laufzeit der Methode durch die Laufzeit des Sortierens dominiert wird. Im letzten Teil der Arbeit haben wir die entwickelten Partitionierungsvefahren für den Aufbau von Geo-Histogrammen eingesetzt, da diese ähnlich zu R-Bäumen eine disjunkte Partitionierung des Raums erzeugen. Ergebnisse von intensiven Experimenten zeigen, dass sich unter Verwendung von neuen Partitionierungstechniken sowohl R-Bäume mit besserer Anfrageperformanz als auch Geo-Histogrammen mit besserer Schätzqualität im Vergleich zu Konkurrenzverfahren generieren lassen.

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