Generalization of Family Operations on ZDDs

Abstract

A family of sets is a collection where each element is a set, enabling the representation of many practical concepts. Various operations on families of sets are widely applied in fields such as databases and data mining. Since the size of set families in these applications often becomes exponentially large, we need sophisticated algorithms to manipulate them. Zero-suppressed decision diagrams (ZDDs) efficiently represent families of sets using directed acyclic graphs, supporting various operations known as family algebra. However, designing efficient algorithms for ZDDs demands expertise and is costly, underscoring the need for more accessible design methods.

This paper introduces an algorithm template that extends ZDD-based family algebra. We can easily design new operations by setting component functions to the template. The template is a natural generalization of existing operations, reproducing them without loss of efficiency. Additionally, it enables the generation of previously impractical ZDD operations without deep knowledge of ZDDs. This paper also presents concrete examples of new operations.