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Approximating Private Set Union/Intersection Cardinality With Logarithmic Complexity
2017
IEEE Transactions on Information Forensics and Security
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The computation of private set union/intersection cardinality (PSU-CA/PSI-CA) is one of the most intensively studied problems in Privacy Preserving Data Mining (PPDM). ...
The protocol has logarithmic computational/communication complexity and relies mostly on symmetric key operations. Thus, it is much more efficient and scalable than existing protocols. ...
First, unlike all existing protocols, our protocol has computational and communication complexities logarithmic in N , the maximum possible cardinality of the private sets 1 . ...
doi:10.1109/tifs.2017.2721360
fatcat:ue6q3ojrxbgd7bf26pqfxhiq5a
Optimization of Bootstrapping in Circuits
2017
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
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In all currently known FHE schemes, encryptions are associated with some (non-negative integer) noise level. At each evaluation of an AND gate, this noise level increases. ...
In this paper, we (1) formally define the bootstrap problem, (2) design a polynomial-time L-approximation algorithm using a novel method of rounding of a linear program, and (3) show a matching hardness ...
However, this does not seem to help for the bootstrap problem, mainly because the family of interesting paths is not closed under union, intersection, and difference. ...
doi:10.1137/1.9781611974782.160
dblp:conf/soda/BenhamoudaLMZ17
fatcat:6f2wwtmcbrd2hnvpdakf3ncrou
Optimization of Bootstrapping in Circuits
[article]
2016
arXiv
pre-print
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In this paper, we formally define the bootstrap problem, we design a polynomial-time L-approximation algorithm using a novel method of rounding of a linear program, and we show a matching hardness result ...
However this does not seem to help for the bootstrap problem, mainly because the family of interesting paths is not closed under union, intersection, and difference. ...
We perform a rounding for each function separately and obtain L sets of marked vertices. By taking the union of these sets, we obtain a feasible solution of cardinality at most L · OPT. Remark. ...
arXiv:1608.04535v1
fatcat:6l5mvfub6bcufi4viyxydg32ce
On the algebra of data sketches
2021
Proceedings of the VLDB Endowment
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of sets from two locations) and what is their total size (intersection of weighted sets). ...
In this paper we propose a sketch that allows to efficiently summarize sets constructed from a sequence of set theory operations. ...
A more sophisticated method of using HyperLogLog sketches to estimate the cardinality of the union, intersection and relative complement has been proposed in [23] . ...
doi:10.14778/3461535.3461553
dblp:journals/pvldb/Lemiesz21
fatcat:ujn3l627yzfdbnor4r6uvbweia
Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling
[article]
2021
arXiv
pre-print
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With |X| as parameter, we show that this is one of the first natural problems to be complete for the complexity class W[3]. ...
Our algorithm is oblivious to k^*, a quantity that is hard to compute or even approximate. ...
Regarding the time complexity, we assume that all set operations (membership, product, union, intersection, and difference) are implemented such that they take time proportional to the total number of ...
arXiv:1805.01310v3
fatcat:zm626hj75javxjnay5it4ligse
Roaring bitmaps: Implementation of an optimized software library
2018
Software, Practice & Experience
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They represent sets and often support operations such as unions, intersections, differences, and symmetric differences. ...
with borrow") to modify the cardinality counter according to the carry flag eventually set by bts. ...
This percentage should be viewed as a rough approximation. ...
doi:10.1002/spe.2560
fatcat:5fryxt7ztbdc3bkzelzquuyfsq
Verified Computational Differential Privacy with Applications to Smart Metering
2013
2013 IEEE 26th Computer Security Foundations Symposium
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This enhanced framework allows us to express a broader range of security properties, that notably include approximate and computational differential privacy. ...
We report on a significantly enhanced version of EasyCrypt that accommodates a richer, user-extensible language of probabilistic expressions and, more fundamentally, supports reasoning about approximate ...
We declare and axiomatize set-theoretical constants and operators over event A , including union, intersection, complement, singleton sets, and constants denoting the empty set and the entire sample space ...
doi:10.1109/csf.2013.26
dblp:conf/csfw/BartheDGKB13
fatcat:m4ur6e3puzbqvaobj44qgkj2ei
An Algorithm for Handling Many Relational Calculus Queries Efficiently
2002
Journal of computer and system sciences (Print)
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Union, Intersection, Set-Subtraction, Projection, Division, Selection, Cross-Product and Join). It turns out that E-RCS formalism is fully adequate for this purpose. ...
T kÀ1 are sets with cardinality no larger than say T k . ...
doi:10.1006/jcss.2002.1848
fatcat:5mjexsxk5rhlpgcxmf6vqnzxha
Privacy-Aware Visualization of Volunteered Geographic Information (VGI) to Analyze Spatial Activity: A Benchmark Implementation
2020
ISPRS International Journal of Geo-Information
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Addressing these privacy conflicts is particularly problematic in natural resource management, where visualizations are often explorative, with multifaceted and sometimes initially unknown sets of analysis ...
While HLL alone cannot preserve privacy, it can be combined with existing approaches to improve privacy while, at the same time, maintaining some flexibility of analysis. ...
Privacy Trade-Off The union -intersection capability of HLL opens up an increased utility of data, but at the same time introduces the possibility of intersection attacks (see Section 4.3). ...
doi:10.3390/ijgi9100607
fatcat:mo323vm23bdznoxgns732ry6dq
Introduction to the Theory of Complexity
1995
Journal of the Operational Research Society
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The Cartesian product of two sets A and B, denoted as A × B, is the set of all ordered pairs x, y with x ∈ A and y ∈ B. Any subset R of A × B is called a binary relation between A and B. ...
In the following chapters, we shall use the term 'relation' to denote both the set of ordered pairs R and the predicate associated with it. ...
Acknowledgements This book originated from a course on Algorithms and Complexity given at the University of Rome 'La Sapienza' by D.P. Bovet and P. Crescenzi since 1986. ...
doi:10.1057/jors.1995.211
fatcat:rx2m7i3vyreaflkxrbmuh5kbhu
Multidimensioned Approaches to Welfare Analysis
[chapter]
1999
Handbook of Income Inequality Measurement
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The test of SSD then requires an appeal to union intersection technique which results in a test procedure with maximum asymptotic size of α if the test statistic at each x is compared with the critical ...
To control for the size of a sequence of tests at several points the Union Intersection (UI) test and Studentized Maximum Modulus technique for multiple comparisons is generally favored in this area. ...
doi:10.1007/978-94-011-4413-1_16
fatcat:r4s5fu77l5ahhdl22dteksx4ty
Identifying patterns in spatial information: A survey of methods
2011
Wiley Interdisciplinary Reviews Data Mining and Knowledge Discovery
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TABLE 1 1 Common Relationships among Nonspatial and Spatial Data
Nonspatial Relationship
Spatial Relationship
Arithmetic
Set-oriented: union, intersection,
membership, . . . ...
Set-based space uses the basic notion of elements, element-equality, sets, and membership to formalize set relationships such as set-equality, subset, union, cardinality, relation, function, and convexity ...
doi:10.1002/widm.25
fatcat:xqcn7cf5bnbevlm2xlhvpr2gle
Complexity Lower Bounds using Linear Algebra
2007
Foundations and Trends® in Theoretical Computer Science
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In these models, we allow unbounded fanin and assume that the operations from the basis are naturally extendable to an unbounded number of operands (e.g., union, intersection, and symmetric difference ...
to compute, or even to approximate well, the communication complexity. ...
Now, the condition is that i.e., an input assignment "picks" either U 1 i or U 0 i depending on whether it sets x i to 1 or 0, respectively, and the function evaluates to 1 on that assignment if and only ...
doi:10.1561/0400000011
fatcat:jso5gaqnhnbitierw4ytzhixna
Information Decomposition Diagrams Applied beyond Shannon Entropy: A Generalization of Hu's Theorem
[article]
2024
arXiv
pre-print
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2022 pre-print arXiv:2202.09393v1 fatcat:joh6pqlr4rdujet6rjgtaiklz4Other Versions
Our result implies for Chaitin's Kolmogorov complexity that the interaction complexities of all degrees are in expectation close to Shannon interaction information. ...
This is answered by Hu's theorem, which is widely known in the form of information diagrams: it relates shapes in a Venn diagram to information functions, thus establishing a bridge from set theory to ...
Hu's theorem (Hu, 1962; Yeung, 1991; renders all this mathematically precise by connecting the set-theoretic operations of union, intersection, and set difference to joint information, interaction information ...
arXiv:2202.09393v3
fatcat:puedltubsfeytlxt4ca6simrdu
Parallel Data Distribution Management on Shared-Memory Multiprocessors
[article]
2019
arXiv
pre-print
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The problem of identifying intersections between two sets of d-dimensional axis-parallel rectangles appears frequently in the context of agent-based simulation studies. ...
HLA) specification -- a standard framework for interoperability among simulators -- includes a Data Distribution Management (DDM) service whose responsibility is to report all intersections between a set ...
Bit vectors allow union, intersection and set difference to be realized efficiently using nothing more than Boolean operators; however, bit vectors require considerable amounts of memory if the number ...
arXiv:1911.03456v1
fatcat:lhphvro2nzfftongd7szwv2soy
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