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DOI: 10.4230/LIPIcs.STACS.2020.30
URN: urn:nbn:de:0030-drops-118911
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11891/
Funakoshi, Mitsuru ; Pape-Lange, Julian
Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements
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Abstract
The discrete acyclic convolution computes the 2n+1 sums ∑_{i+j=k|(i,j)∈[0,1,2,… ,n]²} a_i b_j in 𝒪(n log n) time. By using suitable offsets and setting some of the variables to zero, this method provides a tool to calculate all non-zero sums ∑_{i+j=k|(i,j)∈ P∩ℤ²} a_i b_j in a rectangle P with perimeter p in 𝒪(p log p) time. This paper extends this geometric interpretation in order to allow arbitrary convex polygons P with k vertices and perimeter p. Also, this extended algorithm only needs 𝒪(k + p(log p)² log k) time. Additionally, this paper presents fast algorithms for counting sub-cadences and cadences with 3 elements using this extended method.
BibTeX - Entry
@InProceedings{funakoshi_et_al:LIPIcs:2020:11891,
author = {Mitsuru Funakoshi and Julian Pape-Lange},
title = {{Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements}},
booktitle = {37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
pages = {30:1--30:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-140-5},
ISSN = {1868-8969},
year = {2020},
volume = {154},
editor = {Christophe Paul and Markus Bl{\"a}ser},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/11891},
URN = {urn:nbn:de:0030-drops-118911},
doi = {10.4230/LIPIcs.STACS.2020.30},
annote = {Keywords: discrete acyclic convolutions, string-cadences, geometric algorithms, number theoretic transforms}
}
| Keywords: | discrete acyclic convolutions, string-cadences, geometric algorithms, number theoretic transforms | |
| Seminar: | 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 04.03.2020 |
