The secure dominating set(SDS),a variant of the dominating set,is an important combinatorial structure used in wireless networks.In this paper,we apply algorithmic game theory to study the minimum secure dominating se...The secure dominating set(SDS),a variant of the dominating set,is an important combinatorial structure used in wireless networks.In this paper,we apply algorithmic game theory to study the minimum secure dominating set(Min SDS) problem in a multi-agent system.We design a game framework for SDS and show that every Nash equilibrium(NE) is a minimal SDS,which is also a Pareto-optimal solution.We prove that the proposed game is an exact potential game,and thus NE exists,and design a polynomial-time distributed local algorithm which converges to an NE in O(n) rounds of interactions.Extensive experiments are done to test the performance of our algorithm,and some interesting phenomena are witnessed.展开更多
In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space Lpγ （Rn） to the Lebesgue space Lp（Rn） for 1
基金supported in part by the National Natural Science Foundation of China(U20A2068, 11771013)Zhejiang Provincial Natural Science Foundation of China (LD19A010001)。
文摘The secure dominating set(SDS),a variant of the dominating set,is an important combinatorial structure used in wireless networks.In this paper,we apply algorithmic game theory to study the minimum secure dominating set(Min SDS) problem in a multi-agent system.We design a game framework for SDS and show that every Nash equilibrium(NE) is a minimal SDS,which is also a Pareto-optimal solution.We prove that the proposed game is an exact potential game,and thus NE exists,and design a polynomial-time distributed local algorithm which converges to an NE in O(n) rounds of interactions.Extensive experiments are done to test the performance of our algorithm,and some interesting phenomena are witnessed.
基金supported by National Natural Science Foundation of China (Grant No. 10901017)Program for New Century Excellent Talents in University of China (Grant No. NCET-11-0574) +3 种基金the Fundamental Research Funds for the Central Universitiessupported by National Natural Science Foundation of China (Grant No. 10931001)the Research Fund for the Dectoral Program of Higher Education of China (Grant No. 20090003110018)Program for Changjiang Scholars and Innovative Research Team in University of China
文摘In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space Lpγ （Rn） to the Lebesgue space Lp（Rn） for 1
