Two Topics in Applied Algorithmics Two Topics in Applied Algorithmics Submitted by I Coarse Grained Parallel Computing on Heterogeneous Systems 1

This thesis examines two largely unrelated problems in applied algorithmics, motivated by the search for e cient geometric algorithms. In the rst part of the thesis, we consider the problem of nding e cient parallel algorithms for heterogeneous parallel computers, i.e., parallel computers in which di erent processors have di erent computational potential. To this end, we de ne a formal computational model for heterogeneous systems and develop algorithms for commonly used communication operations. The result is that many existing parallel algorithms which use these communication operations can be adapted to our model with little or no modi cations. In the second part of the thesis we consider the problem of geometric models which allow for varying levels of detail. To this end, we extend the progressive mesh representation introduced by Hoppe. The main technical contribution of this part is an e cient scheme for re ning only selected regions of a progressive mesh. Using this scheme, we develop important applications in the elds of computational geometry and geographic information systems. Both parts of the thesis are supported by experimental results which show that our algorithms are of considerable practical relevance. iii Acknowledgements A number of people have been instrumental in the completion of this thesis, and I would like to acknowledge them here. While writing this thesis I received funding from the Natural Science and Engineering Research Council of Canada and Almerco. It goes without saying that this was greatly appreciated. Jorg Sack has proven to be an excellent supervisor. There are many reasons for this, but the most important of these is his dedication to, and willingness to work for, his students. Anil Maheshwari has provided input on many aspects of this thesis. It is because of his comments and questions that many of the ideas in this thesis are developed to the extent that they are. While writing parts of this thesis, I was lucky to have been a visitor at the Heinz Nixdorf Institut at the Universat GH-Paderborn. During this time, Ben Juurlink gave comments which signi cantly improved the presentation of the rst part of this thesis. Finally I would like to thank Silvia Gotz for having supported me throughout the writing of this thesis, both as a colleague and close friend. For this I am especially grateful. iv