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
To deal with the threat of the new generation of electronic warfare,we establish a non-cooperative countermeasure game model to analyze power allocation and interference suppression between multistatic multipleinput m...To deal with the threat of the new generation of electronic warfare,we establish a non-cooperative countermeasure game model to analyze power allocation and interference suppression between multistatic multipleinput multiple-output(MIMO)radars and multiple jammers in this study.First,according to the power allocation strategy,a supermodular power allocation game framework with a fixed weight(FW)vector is constructed.At the same time,a constrained optimization model for maximizing the radar utility function is established.Based on the utility function,the best power allocation strategies for the radars and jammers are obtained.The existence and uniqueness of the Nash equilibrium(NE)of the supermodular game are proved.A supermodular game algorithm with FW is proposed which converges to the NE.In addition,we use adaptive beamforming methods to suppress cross-channel interference that occurs as direct wave interferences between the radars and jammers.A supermodular game algorithm for joint power allocation and beamforming is also proposed.The algorithm can ensure the best power allocation,and also improves the interference suppression ability of the MIMO radar.Finally,the effectiveness and convergence of two algorithms are verified by numerical results.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 the National Natural Science Foundation of China(No.61372134)。
文摘To deal with the threat of the new generation of electronic warfare,we establish a non-cooperative countermeasure game model to analyze power allocation and interference suppression between multistatic multipleinput multiple-output(MIMO)radars and multiple jammers in this study.First,according to the power allocation strategy,a supermodular power allocation game framework with a fixed weight(FW)vector is constructed.At the same time,a constrained optimization model for maximizing the radar utility function is established.Based on the utility function,the best power allocation strategies for the radars and jammers are obtained.The existence and uniqueness of the Nash equilibrium(NE)of the supermodular game are proved.A supermodular game algorithm with FW is proposed which converges to the NE.In addition,we use adaptive beamforming methods to suppress cross-channel interference that occurs as direct wave interferences between the radars and jammers.A supermodular game algorithm for joint power allocation and beamforming is also proposed.The algorithm can ensure the best power allocation,and also improves the interference suppression ability of the MIMO radar.Finally,the effectiveness and convergence of two algorithms are verified by numerical results.
