Outer Set Operations of Table Algebra of Infinite Tables

2016 ◽  
pp. 011-016
Author(s):  
I.N. Glushko ◽  
Keyword(s):  
Set Operations ◽  
Table Algebra ◽  
Mathematical Semantics

Table algebra of infinite tables is considered. The signature of table algebra of infinite tables is filled up with outer set operations. A formal mathematical semantics of these operations is defined.

scholarly journals A Set of Integral Grid-Coding Algebraic Operations Based on GeoSOT-3D

2021 ◽  
Vol 10 (7) ◽  
pp. 489
Author(s):  
Kaihua Hou ◽  
Chengqi Cheng ◽  
Bo Chen ◽  
Chi Zhang ◽  
Liesong He ◽  
...  
Keyword(s):  
Real Time ◽  
Spatial Information ◽  
Data Retrieval ◽  
Geospatial Data ◽  
Algebraic Operation ◽  
Real Time Processing ◽  
C Language ◽  
Time Processing ◽  
Binary Operations ◽  
Set Operations

As the amount of collected spatial information (2D/3D) increases, the real-time processing of these massive data is among the urgent issues that need to be dealt with. Discretizing the physical earth into a digital gridded earth and assigning an integral computable code to each grid has become an effective way to accelerate real-time processing. Researchers have proposed optimization algorithms for spatial calculations in specific scenarios. However, a complete set of algorithms for real-time processing using grid coding is still lacking. To address this issue, a carefully designed, integral grid-coding algebraic operation framework for GeoSOT-3D (a multilayer latitude and longitude grid model) is proposed. By converting traditional floating-point calculations based on latitude and longitude into binary operations, the complexity of the algorithm is greatly reduced. We then present the detailed algorithms that were designed, including basic operations, vector operations, code conversion operations, spatial operations, metric operations, topological relation operations, and set operations. To verify the feasibility and efficiency of the above algorithms, we developed an experimental platform using C++ language (including major algorithms, and more algorithms may be expanded in the future). Then, we generated random data and conducted experiments. The experimental results show that the computing framework is feasible and can significantly improve the efficiency of spatial processing. The algebraic operation framework is expected to support large geospatial data retrieval and analysis, and experience a revival, on top of parallel and distributed computing, in an era of large geospatial data.

Continuity and identity laws in the axiomatic basis of fuzzy set operations

1997 ◽  
Vol 89 (1) ◽  
pp. 121-124
Author(s):  
Xu Liqun
Keyword(s):  
Fuzzy Set ◽  
Set Operations

Efficient and secure protocols for privacy-preserving set operations

2009 ◽  
Vol 13 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Yingpeng Sang ◽  
Hong Shen
Keyword(s):  
Privacy Preserving ◽  
Set Operations ◽  
Secure Protocols

Set Operations

2016 ◽  
pp. 99-128
Author(s):  
Clare Churcher
Keyword(s):  
Set Operations

Set operations of fuzzy sets using gradual elements

2019 ◽  
Vol 24 (2) ◽  
pp. 879-893
Author(s):  
Hsien-Chung Wu
Keyword(s):  
Fuzzy Sets ◽  
Set Operations

scholarly journals Robust set operations on polyhedral solids

1989 ◽  
Vol 9 (6) ◽  
pp. 50-59 ◽  
Author(s):  
C.M. Hoffmann ◽  
J.E. Hopcroft ◽  
M.J. Karasick
Keyword(s):  
Set Operations

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.

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