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Algorithms 2018, 11(8), 128; https://doi.org/10.3390/a11080128

DenseZDD: A Compact and Fast Index for Families of Sets

1
Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8654, Japan
2
Graduate School of Science and Technology, Nara Institute of Science and Technology, Ikoma 630-0192, Japan
3
Department of Computational Biology and Medical Sciences, Graduate School of Frontier Sciences, The University of Tokyo, Tokyo 113-8654, Japan
4
Graduate School of IST, Hokkaido University, Sapporo 060-0808, Japan
5
Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
This paper is an extended version of our paper published in the 13th International Symposium on Experimental Algorithms (SEA 2014).
*
Author to whom correspondence should be addressed.
Received: 31 May 2018 / Revised: 4 August 2018 / Accepted: 9 August 2018 / Published: 17 August 2018
(This article belongs to the Special Issue Efficient Data Structures)
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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. View Full-Text
Keywords: zero-suppressed binary decision diagram; succinct data structure; set family zero-suppressed binary decision diagram; succinct data structure; set family
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Denzumi, S.; Kawahara, J.; Tsuda, K.; Arimura, H.; Minato, S.-I.; Sadakane, K. DenseZDD: A Compact and Fast Index for Families of Sets . Algorithms 2018, 11, 128.

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