Efficient Algorithms for Coastal Geographic Problems

The increasing performance of computers has made it possible to solve algorithmically problems for which manual and possibly inaccurate methods have been previously used. Nevertheless, one must still pay attention to the performance of an algorithm if huge datasets are used or if the problem iscomputationally difficult. Two geographic problems are studied in the articles included in this thesis. In the first problem the goal is to determine distances from points, called study points, to shorelines in predefined directions. Together with other in-formation, mainly related to wind, these distances can be used to estimate wave exposure at different areas. In the second problem the input consists of a set of sites where water quality observations have been made and of the results of the measurements at the different sites. The goal is to select a subset of the observational sites in such a manner that water quality is still measured in a sufficient accuracy when monitoring at the other sites is stopped to reduce economic cost. Most of the thesis concentrates on the first problem, known as the fetch length problem. The main challenge is that the two-dimensional map is represented as a set of polygons with millions of vertices in total and the distances may also be computed for millions of study points in several directions. Efficient algorithms are developed for the problem, one of them approximate and the others exact except for rounding errors. The solutions also differ in that three of them are targeted for serial operation or for a small number of CPU cores whereas one, together with its further developments, is suitable also for parallel machines such as GPUs.