<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This paper deals with a generalization of polyominoes called (<italic>a, b</italic>)<italic>-connected discrete figures</italic>, where <italic>a</italic> and <italic>b</italic> respectively denotes the connectivity of the foreground (i.e. <italic>black pixels</italic>) and background (i.e. <italic>white pixels</italic>). Formally, a finite set of pixels <italic>P</italic> is (<italic>a, b</italic>)-connected if <italic>P</italic> is <italic>a</italic>-connected and <italic>P̄</italic> is <italic>b</italic>-connected. By adapting a combinatorial structure enumeration algorithm due to Martin, we successfully generate (<italic>a, b</italic>)-connected discrete figures up to size <italic>n</italic> = 18.</p>
</abstract>

This paper deals with a generalization of polyominoes called (a, b)-connected discrete figures, where a and b respectively denotes the connectivity of the foreground (i.e. black pixels) and background (i.e. white pixels). Formally, a finite set of pixels P is (a, b)-connected if P is a-connected and P̄ is b-connected. By adapting a combinatorial structure enumeration algorithm due to Martin, we successfully generate (a, b)-connected discrete figures up to size n = 18.

On the exhaustive generation of discrete figures with connectivity constraints

Department of Computer Science and Mathematics

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On the exhaustive generation of discrete figures with connectivity constraints"}

This paper deals with a generalization of polyominoes called (a, b)-connected discrete figures, where a and b respectively denotes the connectivity of the...

On the exhaustive generation of discrete figures with connectivity constraints

Published Online: Jun 18, 2022

Page range: 106 - 112

Received: Mar 31, 2022

Accepted: May 15, 2022

DOI: https://doi.org/10.2478/puma-2022-0016

Keywords
algorithm, exhaustive generation, discrete figure, digital geometry

© 2022 Hugo Tremblay et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the exhaustive generation of discrete figures with connectivity constraints

Published Online: Jun 18, 2022

Page range: 106 - 112

Received: Mar 31, 2022

Accepted: May 15, 2022

DOI: https://doi.org/10.2478/puma-2022-0016

Keywordsalgorithm, exhaustive generation, discrete figure, digital geometry

© 2022 Hugo Tremblay et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
algorithm, exhaustive generation, discrete figure, digital geometry