Constructing Q-Ideals for Boolean Semiring Partitioning Using Seeds - Claudia Ledbury Justus; Karin-Therese Howell; Cang Hui (Mathematics)
Semiring partitioning is widely used in mathematics, computer science, and data analysis. The purpose of this paper is to add to the theory of semirings by proposing a novel method to construct Q-ideals for partitioning Boolean semirings. We introduce the set of all seeds—all s-tuples over a particular Boolean algebra—and the notion of their weight and complement. Utilizing this new method for constructing Q-ideals, we develop a nested hierarchical partitioning algorithm based on the weight of selected seeds. Additionally, we determine the maximal semiring homomorphism corresponding to this proposed method.