Abstract
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.
Highlights
Zero-suppressed Binary Decision Diagrams (ZDDs) [1] are data structures which are derived from Binary Decision Diagrams (BDDs) [2] and represent a family of sets in a compressed form using Directed Acyclic Graphs (DAGs)
We have proposed top ZDD to compress a ZDD by regarding it as a DAG
We showed that the size of a top ZDD can be logarithmic of that of the standard ZDD
Summary
Zero-suppressed Binary Decision Diagrams (ZDDs) [1] are data structures which are derived from Binary Decision Diagrams (BDDs) [2] and represent a family of sets (combinatorial sets) in a compressed form using Directed Acyclic Graphs (DAGs). Even if the DAG of a ZDD contains repetitive structures in the height direction, they cannot be shared. In. Section 4, we propose our data structure, Top ZDD, and present the detailed components of Top ZDD, the theoretical analysis of the size, and the implementation method of the operations. We propose top ZDDs, which partition the edges of a ZDD into a spanning tree and other edges called complement edges, and store each of them in a compressed form. The results show that the top ZDDs use less space for most of the input data
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