Host cardinality estimation is an important research field in network management and network security.The host cardinality estimation algorithm based on the linear estimator array is a common method.Existing algorithm...Host cardinality estimation is an important research field in network management and network security.The host cardinality estimation algorithm based on the linear estimator array is a common method.Existing algorithms do not take memory footprint into account when selecting the number of estimators used by each host.This paper analyzes the relationship between memory occupancy and estimation accuracy and compares the effects of different parameters on algorithm accuracy.The cardinality estimating algorithm is a kind of random algorithm,and there is a deviation between the estimated results and the actual cardinalities.The deviation is affected by some systematical factors,such as the random parameters inherent in linear estimator and the random functions used to map a host to different linear estimators.These random factors cannot be reduced by merging multiple estimators,and existing algorithms cannot remove the deviation caused by such factors.In this paper,we regard the estimation deviation as a random variable and proposed a sampling method,recorded as the linear estimator array step sampling algorithm(L2S),to reduce the influence of the random deviation.L2S improves the accuracy of the estimated cardinalities by evaluating and remove the expected value of random deviation.The cardinality estimation algorithm based on the estimator array is a computationally intensive algorithm,which takes a lot of time when processing high-speed network data in a serial environment.To solve this problem,a method is proposed to port the cardinality estimating algorithm based on the estimator array to the Graphics Processing Unit(GPU).Experiments on real-world high-speed network traffic show that L2S can reduce the absolute bias by more than 22%on average,and the extra time is less than 61 milliseconds on average.展开更多
An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is ...An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.展开更多
In modern society,it is necessary to perform some secure computations for private sets between different entities.For instance,two merchants desire to calculate the number of common customers and the total number of u...In modern society,it is necessary to perform some secure computations for private sets between different entities.For instance,two merchants desire to calculate the number of common customers and the total number of users without disclosing their own privacy.In order to solve the referred problem,a semi-quantum protocol for private computation of cardinalities of set based on Greenberger-Horne-Zeilinger(GHZ)states is proposed for the first time in this paper,where all the parties just perform single-particle measurement if necessary.With the assistance of semi-honest third party(TP),two semi-quantum participants can simultaneously obtain intersection cardinality and union cardinality.Furthermore,security analysis shows that the presented protocol can stand against some well-known quantum attacks,such as intercept measure resend attack,entangle measure attack.Compared with the existing quantum protocols of Private Set Intersection Cardinality(PSI-CA)and Private Set Union Cardinality(PSU-CA),the complicated oracle operations and powerful quantum capacities are not required in the proposed protocol.Therefore,it seems more appropriate to implement this protocol with current technology.展开更多
The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special...The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special way.Firstly,a probability density function is assigned for any given HFE.Thereafter,equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function.The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs,the higher the credibility of the mentioned membership degrees is,then,the bigger the probability density values for them are.According to this transformation technique,a set of novel distance measures on HFSs is provided.Finally,an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures.The example also shows that this study is a good complement to operation theories on HFSs.展开更多
The Gibbs-like variational methodology is applied to the heterogeneous systems with rigid pyroelectric or pyromagnetic domains. The processes of depolarization/demagnetization are taken into account by assuming the sp...The Gibbs-like variational methodology is applied to the heterogeneous systems with rigid pyroelectric or pyromagnetic domains. The processes of depolarization/demagnetization are taken into account by assuming the spatial mobility of the interfaces. The simplest configuration of flat interface separating rigid pyroelectric half-spaces permits explicit analysis of morphological stability.展开更多
In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it th...In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of “whole is greater than part”, and created another ruler for measuring infinite sets. The discussion in this paper shows that, compared with the cardinal number method, the Grossone method enables infinity calculation to achieve a leap from qualitative calculation to quantitative calculation. According to Grossone theory, there is neither the largest infinity and infinitesimal, nor the smallest infinity and infinitesimal. Hilbert’s first problem was caused by the immaturity of the infinity theory.展开更多
文摘Host cardinality estimation is an important research field in network management and network security.The host cardinality estimation algorithm based on the linear estimator array is a common method.Existing algorithms do not take memory footprint into account when selecting the number of estimators used by each host.This paper analyzes the relationship between memory occupancy and estimation accuracy and compares the effects of different parameters on algorithm accuracy.The cardinality estimating algorithm is a kind of random algorithm,and there is a deviation between the estimated results and the actual cardinalities.The deviation is affected by some systematical factors,such as the random parameters inherent in linear estimator and the random functions used to map a host to different linear estimators.These random factors cannot be reduced by merging multiple estimators,and existing algorithms cannot remove the deviation caused by such factors.In this paper,we regard the estimation deviation as a random variable and proposed a sampling method,recorded as the linear estimator array step sampling algorithm(L2S),to reduce the influence of the random deviation.L2S improves the accuracy of the estimated cardinalities by evaluating and remove the expected value of random deviation.The cardinality estimation algorithm based on the estimator array is a computationally intensive algorithm,which takes a lot of time when processing high-speed network data in a serial environment.To solve this problem,a method is proposed to port the cardinality estimating algorithm based on the estimator array to the Graphics Processing Unit(GPU).Experiments on real-world high-speed network traffic show that L2S can reduce the absolute bias by more than 22%on average,and the extra time is less than 61 milliseconds on average.
文摘An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.
基金supported by the National Natural Science Foundation of China(61802118)Natural Science Foundation of Heilongjiang Province(YQ2020F013)supported by the Advanced Programs of Heilongjiang Province for the Overseas Scholars and the Outstanding Youth Fund of Heilongjiang University and the Heilongjiang University Innovation Fund(YJSCX2022-247HLJU)
文摘In modern society,it is necessary to perform some secure computations for private sets between different entities.For instance,two merchants desire to calculate the number of common customers and the total number of users without disclosing their own privacy.In order to solve the referred problem,a semi-quantum protocol for private computation of cardinalities of set based on Greenberger-Horne-Zeilinger(GHZ)states is proposed for the first time in this paper,where all the parties just perform single-particle measurement if necessary.With the assistance of semi-honest third party(TP),two semi-quantum participants can simultaneously obtain intersection cardinality and union cardinality.Furthermore,security analysis shows that the presented protocol can stand against some well-known quantum attacks,such as intercept measure resend attack,entangle measure attack.Compared with the existing quantum protocols of Private Set Intersection Cardinality(PSI-CA)and Private Set Union Cardinality(PSU-CA),the complicated oracle operations and powerful quantum capacities are not required in the proposed protocol.Therefore,it seems more appropriate to implement this protocol with current technology.
基金supported by Shanghai Pujiang Program (No.2019PJC062)the Natural Science Foundation of Shandong Province (No.ZR2021MG003)the Research Project on Undergraduate Teaching Reform of Higher Education in Shandong Province (No.Z2021046).
文摘The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special way.Firstly,a probability density function is assigned for any given HFE.Thereafter,equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function.The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs,the higher the credibility of the mentioned membership degrees is,then,the bigger the probability density values for them are.According to this transformation technique,a set of novel distance measures on HFSs is provided.Finally,an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures.The example also shows that this study is a good complement to operation theories on HFSs.
文摘The Gibbs-like variational methodology is applied to the heterogeneous systems with rigid pyroelectric or pyromagnetic domains. The processes of depolarization/demagnetization are taken into account by assuming the spatial mobility of the interfaces. The simplest configuration of flat interface separating rigid pyroelectric half-spaces permits explicit analysis of morphological stability.
文摘In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of “whole is greater than part”, and created another ruler for measuring infinite sets. The discussion in this paper shows that, compared with the cardinal number method, the Grossone method enables infinity calculation to achieve a leap from qualitative calculation to quantitative calculation. According to Grossone theory, there is neither the largest infinity and infinitesimal, nor the smallest infinity and infinitesimal. Hilbert’s first problem was caused by the immaturity of the infinity theory.
