BCube is one kind of important data center networks.Hamiltonicity and Hamiltonian connectivity have significant applications in communication networks.So far,there have been many results concerning fault-tolerant Hami...BCube is one kind of important data center networks.Hamiltonicity and Hamiltonian connectivity have significant applications in communication networks.So far,there have been many results concerning fault-tolerant Hamiltonicity and fault-tolerant Hamiltonian connectivity in some data center networks.However,these results only consider faulty edges and faulty servers.In this paper,we study the fault-tolerant Hamiltonicity and the fault-tolerant Hamiltonian connectivity of BCube(n,k)under considering faulty servers,faulty links/edges,and faulty switches.For any integers n≥2 and k≥0,let BCn,k be the logic structure of BCube(n,k)and F be the union of faulty elements of BCn,k,Let fv/fe,and fs be the number of faulty servers,faulty edges,and faulty switches of BCiLbe(n,k),respectively.We show that BCnik-F is fault-tolerant Hamiltonian if fv+fe+(n-1)/s≤(n-1)(k+1)-2 and BCn,k-F is fault-tolerant Hamiltonian-connected ifv,+fe+(n-1)fs≤(n-1)(k+1)-3.To the best of our knowledge,this paper is the first work which takes faulty switches into account to study the fault-tolerant Hamiltonicity and the fault-tolerant Hamiltonian connectivity in data center networks.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.U1905211,61572337,and 61972272Jiangsu Planned Projects for Postdoctoral Research Funds under Grant No.1701173B+1 种基金Application Foundation Research of Suzhou of China under Grant No.SYG201653a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘BCube is one kind of important data center networks.Hamiltonicity and Hamiltonian connectivity have significant applications in communication networks.So far,there have been many results concerning fault-tolerant Hamiltonicity and fault-tolerant Hamiltonian connectivity in some data center networks.However,these results only consider faulty edges and faulty servers.In this paper,we study the fault-tolerant Hamiltonicity and the fault-tolerant Hamiltonian connectivity of BCube(n,k)under considering faulty servers,faulty links/edges,and faulty switches.For any integers n≥2 and k≥0,let BCn,k be the logic structure of BCube(n,k)and F be the union of faulty elements of BCn,k,Let fv/fe,and fs be the number of faulty servers,faulty edges,and faulty switches of BCiLbe(n,k),respectively.We show that BCnik-F is fault-tolerant Hamiltonian if fv+fe+(n-1)/s≤(n-1)(k+1)-2 and BCn,k-F is fault-tolerant Hamiltonian-connected ifv,+fe+(n-1)fs≤(n-1)(k+1)-3.To the best of our knowledge,this paper is the first work which takes faulty switches into account to study the fault-tolerant Hamiltonicity and the fault-tolerant Hamiltonian connectivity in data center networks.
