Data Structures for Efficient String Algorithms

This thesis deals with data structures that are mostly useful in the area of string matching and string mining. Our main result is an O(n)-time preprocessing scheme for an array of n numbers such that subsequent queries asking for the position of a minimum element in a specified interval can be answered in constant time (so-called RMQs for Range Minimum Queries). The space for this data structure is 2n + o(n) bits, which is shown to be asymptotically optimal in a general setting. This improves all previous results on this problem. The main techniques for deriving this result rely on combinatorial properties of arrays and so-called Cartesian Trees. For compressible input arrays we show that further space can be saved, while not affecting the time bounds. For the two-dimensional variant of the RMQ-problem we give a preprocessing scheme with quasi-optimal time bounds, but with an asymptotic increase in space consumption of a factor of log n. It is well known that algorithms for answering RMQs in constant time ar

Theoretical Bioinformatics Group

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Multi-modal Scene Understanding Using Probabilistic Models

First, I would like to especially thank my advisor, Prof. Gerhard Sagerer, for his openminded support, continual encouragement, and fruitful discussions. His way of mediating experiences beyond technical aspects of research was very inspiring for me. I enjoyed many joint conference visits with him and the cooperative organization of the workshop “Integration of Speech and Image Understanding ” which was associated with the International Conference of Computer Vision 1999. Secondly, I very much acknowledge Prof. Sven Dickinson from the University of Toronto for being the second reviewer in my thesis committee. His comments encourage me to continue research in this area. I have to thank Enno Ohlebusch for his offhanded readiness to substitute Prof. Dickinson during my defence who had to cancel his flight because of the terrorist attack happening in New York, Sept. 2001. The present thesis was embedded in the Collaborative Research Center 360 “Situated Artificial Communicators ” that has been funded by the German Research Foundation. I joined the research project “Interaktion sprachlicher und visueller Informationsverarbeitung” (Interaction of speech and image processing) for three exciting and inspirin