Storing Set Families More Compactly with Top ZDDs

Zero-suppressed Binary Decision Diagrams (ZDDs) are data structures for representing set families in a compressed form. With ZDDs, many valuable operations on set families can be done in time polynomial in ZDD size. In some cases, however, the size of ZDDs for representing large set families becomes too huge to store them in the main memory. This paper proposes top ZDD, a novel representation of ZDDs which uses less space than existing ones. The top ZDD is an extension of the top tree, which compresses trees, to compress directed acyclic graphs by sharing identical subgraphs. We prove that navigational operations on ZDDs can be done in time poly-logarithmic in ZDD size, and show that there exist set families for which the size of the top ZDD is exponentially smaller than that of the ZDD. We also show experimentally that our top ZDDs have smaller sizes than ZDDs for real data.