# MPI-I-94-150

## On characteristic points and approximate decision algorithms for the minimum Hausdorff distance

### Chew, L. P. and Kedem, K. and Schirra, Stefan

**MPI-I-94-150**. September** **1994, 10 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

We investigate {\em approximate decision algorithms} for determining

whether the minimum Hausdorff distance between two points sets (or

between two sets of nonintersecting line segments) is at most

$\varepsilon$.\def\eg{(\varepsilon/\gamma)}

An approximate decision algorithm is a standard decision algorithm

that answers {\sc yes} or {\sc no} except when $\varepsilon$ is in

an {\em indecision interval}

where the algorithm is allowed to answer {\sc don't know}.

We present algorithms with indecision interval

$[\delta-\gamma,\delta+\gamma]$ where $\delta$ is the minimum

Hausdorff distance and $\gamma$ can be chosen by the user.

In other words, we can make our

algorithm as accurate as desired by choosing an appropriate $\gamma$.

For two sets of points (or two sets of nonintersecting lines) with

respective

cardinalities $m$ and $n$ our approximate decision algorithms run in

time $O(\eg^2(m+n)\log(mn))$ for Hausdorff distance under translation,

and in time $O(\eg^2mn\log(mn))$ for Hausdorff distance under

Euclidean motion.

Acknowledgement:** **

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1994-150

**BibTeX**
`@TECHREPORT{``ChewKedernSchirra94``,`

` AUTHOR = {Chew, L. P. and Kedem, K. and Schirra, Stefan},`

` TITLE = {On characteristic points and approximate decision algorithms for the minimum Hausdorff distance},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-94-150},`

` MONTH = {September},`

` YEAR = {1994},`

` ISSN = {0946-011X},`

`}`