| Issue |
RAIRO-Theor. Inf. Appl.
Volume 58, 2024
Randomness and Combinatorics - Edited by Luca Ferrari & Paolo Massazza
|
|
|---|---|---|
| Article Number | 16 | |
| Number of page(s) | 15 | |
| DOI | https://doi.org/10.1051/ita/2024013 | |
| Published online | 28 August 2024 | |
On the generation of discrete figures with connectivity constraints
1
Department of Computer Science and Mathematics, Université du Québec à Chicoutimi, Canada
2
Asobo Studio, France
* Corresponding author: hugo_tremblay2@uqac.ca
Received:
13
December
2022
Accepted:
11
July
2024
This paper addresses a generalization of polyominoes called (a, b)-connected discrete figures, where a and b represent the connectivity of the foreground (i.e. black pixels) and background (i.e. white pixels), respectively. Formally, a finite set of pixels P is (a, b)-connected if P is a-connected and P is b-connected. By adapting a combinatorial structure enumeration algorithm by J. L. Martin and employing breadth-first search ordering on the pixels of the figures, we sequentially generate all (a, b)-connected discrete figures up to size n = 18, utilizing minimal storage space. This paper presents an extended version of the research presented at the 2022 GASCom conference.
Mathematics Subject Classification: 05A15 / 05B50
Key words: Combinatorics / digital geometry / polyominoes / exhaustive generation / algorithmics / parallelization
© The authors. Published by EDP Sciences, 2024
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