scholarly journals DenseZDD: A Compact and Fast Index for Families of Sets

Algorithms ◽  
2018 ◽  
Vol 11 (8) ◽  
pp. 128 ◽  
Author(s):  
Shuhei Denzumi ◽  
Jun Kawahara ◽  
Koji Tsuda ◽  
Hiroki Arimura ◽  
Shin-ichi Minato ◽  
...  
Keyword(s):  
Data Structure ◽  
Data Structures ◽  
Information Integration ◽  
Decision Diagrams ◽  
Web Information Retrieval ◽  
Binary Decision ◽  
Web Information ◽  
Set Operations ◽  
Succinct Data Structure ◽  
The Family

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.

scholarly journals FASTSET: A Fast Data Structure for the Representation of Sets of Integers

Algorithms ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 91
Author(s):  
Giuseppe Lancia ◽  
Marcello Dalpasso
Keyword(s):  
Data Structure ◽  
Data Structures ◽  
Optimal Time ◽  
Time Performance ◽  
Set Operations

We describe a simple data structure for storing subsets of { 0 , … , N − 1 } , with N a given integer, which has optimal time performance for all the main set operations, whereas previous data structures are non-optimal for at least one such operation. We report on the comparison of a Java implementation of our structure with other structures of the standard Java Collections.

scholarly journals Compressing Exact Cover Problems with Zero-suppressed Binary Decision Diagrams

2021 ◽  
Author(s):  
Masaaki Nishino ◽  
Norihito Yasuda ◽  
Kengo Nakamura
Keyword(s):  
Data Structure ◽  
State Of The Art ◽  
Linear Time ◽  
Binary Decision Diagrams ◽  
Experimental Results ◽  
Decision Diagrams ◽  
Binary Decision ◽  
Running Time ◽  
Order Of Magnitude ◽  
Exact Cover

Exact cover refers to the problem of finding subfamily F of a given family of sets S whose universe is D, where F forms a partition of D. Knuth’s Algorithm DLX is a state-of-the-art method for solving exact cover problems. Since DLX’s running time depends on the cardinality of input S, it can be slow if S is large. Our proposal can improve DLX by exploiting a novel data structure, DanceDD, which extends the zero-suppressed binary decision diagram (ZDD) by adding links to enable efficient modifications of the data structure. With DanceDD, we can represent S in a compressed way and perform search in linear time with the size of the structure by using link operations. The experimental results show that our method is an order of magnitude faster when the problem is highly compressed.

Adaptive Ontology-Based Web Information Retrieval

2012 ◽  
pp. 152-170 ◽  
Author(s):  
Cédric Pruski ◽  
Nicolas Guelfi ◽  
Chantal Reynaud
Keyword(s):  
Information Retrieval ◽  
Data Structures ◽  
Web Search ◽  
Relevant Information ◽  
Web Pages ◽  
Web Information Retrieval ◽  
Domain Specific ◽  
Web Information ◽  
Expansion Technique ◽  
The Web

Finding relevant information on the Web is difficult for most users. Although Web search applications are improving, they must be more “intelligent” to adapt to the search domains targeted by queries, the evolution of these domains, and users’ characteristics. In this paper, the authors present the TARGET framework for Web Information Retrieval. The proposed approach relies on the use of ontologies of a particular nature, called adaptive ontologies, for representing both the search domain and a user’s profile. Unlike existing approaches on ontologies, the authors make adaptive ontologies adapt semi-automatically to the evolution of the modeled domain. The ontologies and their properties are exploited for domain specific Web search purposes. The authors propose graph-based data structures for enriching Web data in semantics, as well as define an automatic query expansion technique to adapt a query to users’ real needs. The enriched query is evaluated on the previously defined graph-based data structures representing a set of Web pages returned by a usual search engine in order to extract the most relevant information according to user needs. The overall TARGET framework is formalized using first-order logic and fully tool supported.

scholarly journals Storing Set Families More Compactly with Top ZDDs

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 172
Author(s):  
Kotaro Matsuda ◽  
Shuhei Denzumi ◽  
Kunihiko Sadakane
Keyword(s):  
Data Structures ◽  
Binary Decision Diagrams ◽  
Real Data ◽  
Directed Acyclic Graphs ◽  
Main Memory ◽  
Large Set ◽  
Decision Diagrams ◽  
Binary Decision ◽  
Acyclic Graphs

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.

scholarly journals Genetic algorithm for binary and functional decision diagrams optimization

2018 ◽  
Vol 31 (2) ◽  
pp. 169-187
Author(s):  
Stojkovic Suzana ◽  
Velickovic Darko ◽  
Moraga Claudio
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Data Structure ◽  
Optimization Problems ◽  
Binary Decision Diagrams ◽  
Size Optimization ◽  
Decision Diagrams ◽  
Crossover Operator ◽  
Binary Decision ◽  
Discrete Functions

Decision diagrams (DD) are a widely used data structure for discrete functions representation. The major problem in DD-based applications is the DD size minimization (reduction of the number of nodes), because their size is dependent on the variables order. Genetic algorithms are often used in different optimization problems including the DD size optimization. In this paper, we apply the genetic algorithm to minimize the size of both Binary Decision Diagrams (BDDs) and Functional Decision Diagrams (FDDs). In both cases, in the proposed algorithm, a Bottom-Up Partially Matched Crossover (BU-PMX) is used as the crossover operator. In the case of BDDs, mutation is done in the standard way by variables exchanging. In the case of FDDs, the mutation by changing the polarity of variables is additionally used. Experimental results of optimization of the BDDs and FDDs of the set of benchmark functions are also presented.

Adaptive Ontology-Based Web Information Retrieval

2011 ◽  
Vol 3 (3) ◽  
pp. 41-58 ◽  
Author(s):  
Cédric Pruski ◽  
Nicolas Guelfi ◽  
Chantal Reynaud
Keyword(s):  
Information Retrieval ◽  
Data Structures ◽  
Web Search ◽  
Relevant Information ◽  
Web Pages ◽  
Web Information Retrieval ◽  
Domain Specific ◽  
Web Information ◽  
Expansion Technique ◽  
Search Domain

Finding relevant information on the Web is difficult for most users. Although Web search applications are improving, they must be more “intelligent” to adapt to the search domains targeted by queries, the evolution of these domains, and users’ characteristics. In this paper, the authors present the TARGET framework for Web Information Retrieval. The proposed approach relies on the use of ontologies of a particular nature, called adaptive ontologies, for representing both the search domain and a user’s profile. Unlike existing approaches on ontologies, the authors make adaptive ontologies adapt semi-automatically to the evolution of the modeled domain. The ontologies and their properties are exploited for domain specific Web search purposes. The authors propose graph-based data structures for enriching Web data in semantics, as well as define an automatic query expansion technique to adapt a query to users’ real needs. The enriched query is evaluated on the previously defined graph-based data structures representing a set of Web pages returned by a usual search engine in order to extract the most relevant information according to user needs. The overall TARGET framework is formalized using first-order logic and fully tool supported.

scholarly journals Group Decision Diagram (GDD): A Compact Representation for Permutations

2019 ◽  
Vol 33 ◽  
pp. 2986-2994
Author(s):  
Takanori Maehara ◽  
Yuma Inoue
Keyword(s):  
Artificial Intelligence ◽  
Data Structure ◽  
Permutation Group ◽  
Group Decision ◽  
Cartesian Product ◽  
Compact Representation ◽  
Combinatorial Object ◽  
Binary Decision ◽  
Set Operations ◽  
Set Of Permutations

Permutation is a fundamental combinatorial object appeared in various areas in mathematics, computer science, and artificial intelligence. In some applications, a subset of a permutation group must be maintained efficiently. In this study, we develop a new data structure, called group decision diagram (GDD), to maintain a set of permutations. This data structure combines the zero-suppressed binary decision diagram with the computable subgroup chain of the permutation group. The data structure enables efficient operations, such as membership testing, set operations (e.g., union, intersection, and difference), and Cartesian product. Our experiments demonstrate that the data structure is efficient (i.e., 20–300 times faster) than the existing methods when the permutation group is considerably smaller than the symmetric group, or only subsets constructed by a few operations over generators are maintained.

scholarly journals BDD-based verification of scalable designs

2007 ◽  
Vol 20 (3) ◽  
pp. 367-379
Author(s):  
Daniel Große ◽  
Rolf Drechsler
Keyword(s):  
Data Structure ◽  
Decision Diagrams ◽  
Binary Decision ◽  
Verification Algorithm ◽  
Word Level ◽  
Variable Ordering ◽  
Level Data ◽  
Level Information ◽  
Speed Up ◽  
Verification Techniques

Many formal verification techniques make use of Binary Decision Diagrams (BDDs). In most applications the choice of the variable ordering is crucial for the performance of the verification algorithm. Usually BDDs operate on the Boolean level, i.e. BDDs are a bit-level data structure. In this paper we present a method to speed-up BDD-based verification of scalable designs that makes use of a learning process for word-level information. In a pre-processing a scalable ordering is extracted from the RTL that is used as a static ordering for large designs. Experimental results show that significant improvements can be achieved.

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