MPI-INF/SWS Research Reports 1991-2021

# 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

#### September 1994, 10 pages.

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##### Status: available - back from printing

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.

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URL to this document: https://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},