On the generation of discrete figures with connectivity constraints

Abstract

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.