License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2020.32
URN: urn:nbn:de:0030-drops-133760
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13376/
Aronov, Boris ;
Cardinal, Jean
Geometric Pattern Matching Reduces to k-SUM
Abstract
We prove that some exact geometric pattern matching problems reduce in linear time to o k-SUM when the pattern has a fixed size k. This holds in the real RAM model for searching for a similar copy of a set of k ≥ 3 points within a set of n points in the plane, and for searching for an affine image of a set of k ≥ d+2 points within a set of n points in d-space.
As corollaries, we obtain improved real RAM algorithms and decision trees for the two problems. In particular, they can be solved by algebraic decision trees of near-linear height.
BibTeX - Entry
@InProceedings{aronov_et_al:LIPIcs:2020:13376,
author = {Boris Aronov and Jean Cardinal},
title = {{Geometric Pattern Matching Reduces to k-SUM}},
booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)},
pages = {32:1--32:9},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-173-3},
ISSN = {1868-8969},
year = {2020},
volume = {181},
editor = {Yixin Cao and Siu-Wing Cheng and Minming Li},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13376},
URN = {urn:nbn:de:0030-drops-133760},
doi = {10.4230/LIPIcs.ISAAC.2020.32},
annote = {Keywords: Geometric pattern matching, k-SUM problem, Linear decision trees}
}
|
Keywords: |
|
Geometric pattern matching, k-SUM problem, Linear decision trees |
|
Collection: |
|
31st International Symposium on Algorithms and Computation (ISAAC 2020) |
|
Issue Date: |
|
2020 |
|
Date of publication: |
|
04.12.2020 |
