Fault-Tolerant Hamiltonicity and Hamiltonian Connectivity of BCube with Various Faulty Elements

• 作 者: Gui-Juan Wang Cheng-Kuan Lin Jian-Xi Fan Jing-Ya Zhou Bao-Lei Cheng
• 机 构: School of Computer Science and Technology,Soochow University,Suzhou 215006,China;School of Computer
• 出 处: 计算机科学技术学报（英文版）
• 发表日期: 2020年5期
• 关键词: data center network BCube fault-tolerance Hamiltonicity Hamiltonian connectivity

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 BCube(n,k),respectively.We show that BCn,k-F is fault-tolerant Hamiltonian if fv + fe + (n-1)fs ≤ (n-1)(k + 1)-2 and BCn,k-F is fault-tolerant Hamiltonian-connected if fv + 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.