Article ID: | iaor201113543 |
Volume: | 38 |
Issue: | 1 |
Start Page Number: | 131 |
End Page Number: | 143 |
Publication Date: | Jan 2004 |
Journal: | Algorithmica |
Authors: | Daescu Ovidiu |
Keywords: | programming: geometric |
In this paper we give bounds on the complexity of some algorithms for approximating 2‐D and 3‐D polygonal paths with the infinite beam measure of error. While the time/space complexities of the algorithms known for other error measures are well understood, path approximation with infinite beam measure seems to be harder due to the complexity of some geometric structures that arise in the known approaches. Our results answer some open problems left in previous work. We also present a more careful analysis of the time complexity of the general iterative algorithm for infinite beam measure and show that it could perform much better in practice than in the worst case. We then propose a new approach for path approximation that consists of a breadth first traversal of the path approximation graph, without constructing the graph. This approach can be applied to any error criterion in any constant dimension. The running time of the new algorithm depends on the size of the output: if the optimal approximating path has