2024/04/23 by Hiromi Emoto, Emoto, Hiromi, Yuni Iwamasa +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2404.14670
openalex publication_date 2024/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Matroids are often represented as oracles since there are no unified and compact representations for general matroids. This paper initiates the study of binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) as relatively compact data structures for representing matroids in a computer. This study particularly focuses on the sizes of BDDs and ZDDs representing matroids. First, we compare the sizes of different variations of BDDs and ZDDs for a matroid. These comparisons involve concise transformations between specific decision diagrams. Second, we provide upper bounds on the size of BDDs and ZDDs for several classes of matroids. These bounds are closely related to the number of minors of the matroid and depend only on the connectivity function or pathwidth of the matroid, which deeply relates to the classes of matroids called strongly pigeonhole classes. In essence, these results indicate upper bounds on the number of minors for specific classes of matroids and new strongly pigeonhole classes.