## The Directed Hausdorff Distance between Imprecise Point Sets

We consider the directed Hausdorff distance between point sets in the plane, where one or both point sets consist of imprecise points. An imprecise point is modelled by a disc given by its centre and a radius. The actual position of an imprecise point may be anywhere within its disc. Due to the direction of the Hausdorff Distance and whether its tight upper or lower bound is computed there are several cases to consider. For every case we either show that the computation is NP-hard or we present an algorithm with a polynomial running time. Further we give several approximation algorithms for the hard cases and show that one of them cannot be approximated better than with factor 3, unless P=NP.

keywords: Computational Geometry, Data Imprecision

### Journal Article (peer-reviewed)

Christian Knauer, Maarten Löffler, Marc Scherfenberg, Thomas Wolle

The Directed Hausdorff Distance between Imprecise Point Sets

Theoretical Computer Science

412, 32, 4173–4186, 2011

### Conference Proceedings (peer-reviewed)

Christian Knauer, Maarten Löffler, Marc Scherfenberg, Thomas Wolle

The Directed Hausdorff Distance between Imprecise Point Sets

Proc. 20th International Symposium on Algorithms and Computation

LNCS 5878, 720–729, 2009

*Invited to Special Issue of TCS*

### Archived Publication (not reviewed)

Christian Knauer, Maarten Löffler, Marc Scherfenberg, Thomas Wolle

The Directed Hausdorff Distance between Imprecise Point Sets

0909.4642, 2009

back to list