Abstract
In this article, we propose a succinct data structure of zero-suppressed binary decision diagrams (ZDDs). A ZDD represents sets of combinations efficiently and we can perform various set operations on the ZDD without explicitly extracting combinations. Thanks to these features, ZDDs have been applied to web information retrieval, information integration, and data mining. However, to support rich manipulation of sets of combinations and update ZDDs in the future, ZDDs need too much space, which means that there is still room to be compressed. The paper introduces a new succinct data structure, called DenseZDD, for further compressing a ZDD when we do not need to conduct set operations on the ZDD but want to examine whether a given set is included in the family represented by the ZDD, and count the number of elements in the family. We also propose a hybrid method, which combines DenseZDDs with ordinary ZDDs. By numerical experiments, we show that the sizes of our data structures are three times smaller than those of ordinary ZDDs, and membership operations and random sampling on DenseZDDs are about ten times and three times faster than those on ordinary ZDDs for some datasets, respectively.
Highlights
A Binary Decision Diagram (BDD) [1] is a graph-based representation of a Boolean function, widely used in very-large-scale integration (VLSI) logic design, verification, and so on
The main updates of this paper from the previous version are as follows: (i) we propose algorithms for counting and fast random sampling on DenseZDD; (ii) we propose a static representation of a variant of zero-suppressed binary decision diagrams (ZDDs) called Sequence BDD; and (iii) we conduct more experiments on new large data sets using algorithms
The size of the hash table of SAPPOROBDD is 5 × 2 × n bytes, and 5 bytes per each node to chain ZDD nodes that have the same key computed from its attribute-triple
Summary
A Binary Decision Diagram (BDD) [1] is a graph-based representation of a Boolean function, widely used in very-large-scale integration (VLSI) logic design, verification, and so on. This paper proposes a succinct data structure of ZDDs, which we call DenseZDDs, which support only static operations. Experimental results show that the sizes of our data structures are three times smaller than those of ordinary ZDDs, and membership operations and random sampling on DenseZDDs are about ten times and three times faster than those on ordinary. The main updates of this paper from the previous version are as follows: (i) we propose algorithms for counting and fast random sampling on DenseZDD; (ii) we propose a static representation of a variant of ZDDs called Sequence BDD; and (iii) we conduct more experiments on new large data sets using algorithms (including new proposed ones).
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