We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness constraint.This sum function is non-submodular in general.For an offline model,we introduce two approximation ...We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness constraint.This sum function is non-submodular in general.For an offline model,we introduce two approximation algorithms:A greedy algorithm and a threshold greedy algorithm.For a streaming model,we propose a one-pass streaming algorithm.We also analyze the approximation ratios of these algorithms,which all depend on the total curvature of the supermodular function.The total curvature is computable in polynomial time and widely utilized in the literature.展开更多
The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plan...The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this method.展开更多
The clustering problem of big data in the era of artificial intelligence has been widely studied.Because of the huge amount of data,distributed algorithms are often used to deal with big data problems.The distributed ...The clustering problem of big data in the era of artificial intelligence has been widely studied.Because of the huge amount of data,distributed algorithms are often used to deal with big data problems.The distributed computing model has an attractive feature:it can handle massive datasets that cannot be put into the main memory.On the other hand,since many decisions are made automatically by machines in today’s society,algorithm fairness is also an important research area of machine learning.In this paper,we study two fair clustering problems:the centralized fair k-center problem with outliers and the distributed fair k-center problem with outliers.For these two problems,we have designed corresponding constant approximation ratio algorithms.The theoretical proof and analysis of the approximation ratio,and the running space of the algorithm are given.展开更多
基金The first author was supported by the National Natural Science Foundation of China(Nos.12001025 and 12131003)The second author was supported by the Spark Fund of Beijing University of Technology(No.XH-2021-06-03)+2 种基金The third author was supported by the Natural Sciences and Engineering Research Council of Canada(No.283106)the Natural Science Foundation of China(Nos.11771386 and 11728104)The fourth author is supported by the National Natural Science Foundation of China(No.12001335).
文摘We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness constraint.This sum function is non-submodular in general.For an offline model,we introduce two approximation algorithms:A greedy algorithm and a threshold greedy algorithm.For a streaming model,we propose a one-pass streaming algorithm.We also analyze the approximation ratios of these algorithms,which all depend on the total curvature of the supermodular function.The total curvature is computable in polynomial time and widely utilized in the literature.
基金Supported by Hi -tech Research and Development Program of China(No. 2001AA421200).
文摘The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this method.
基金This work was supported by the National Natural Science Foundation of China(Nos.12131003,11771386,and 11728104)the Beijing Natural Science Foundadtion Project(No.Z200002)+2 种基金the General Research Projects of Beijing Educations Committee in China(No.KM201910005013)the Natural Sciences and Engineering Research Council of Canada(NSERC)(No.06446)the General Program of Science and Technology Development Project of Beijing Municipal Education Commission(No.KM201810005005).
文摘The clustering problem of big data in the era of artificial intelligence has been widely studied.Because of the huge amount of data,distributed algorithms are often used to deal with big data problems.The distributed computing model has an attractive feature:it can handle massive datasets that cannot be put into the main memory.On the other hand,since many decisions are made automatically by machines in today’s society,algorithm fairness is also an important research area of machine learning.In this paper,we study two fair clustering problems:the centralized fair k-center problem with outliers and the distributed fair k-center problem with outliers.For these two problems,we have designed corresponding constant approximation ratio algorithms.The theoretical proof and analysis of the approximation ratio,and the running space of the algorithm are given.
