Hamiltonian Analysis Of Network Structure Based On Basic Elements

At present,the application of cloud computing is more and more widely,It mainly distributes those complicated and difficult computing to a large number of distributed computers to calculate,so that the ability of the "cloud" side is continuously improved.And large data center networks are the foundation of cloud computing.Hamiltonian is one of the indicators to measure the performance of data center network structure,If Hamilton path is used in multicast algorithm,the congestion and deadlock caused by traditional tree-based multicast algorithm can be reduced.Hamiltonian paths in the network structure can make the network communicate more efficiently.Therefore,by deeply studying the Hamiltonian of classical data center network structure,it is proposed that the element-based network structure is a sufficient condition for Hamiltonian connectivity and the network structure contains nodes with degree 2,and there is no Hamiltonian and so on.The main research results are as follows:(1)After summarizing and analyzing the other network structure's proof of Hamiltonian,it is proposed that the network structure based on the basic element satisfies the three conditions of recursion,connectivity and the minimum number of edges of the cut is greater than or equal to 4,which indicates that the network structure has Hamiltonian property.At the same time,this theorem is discussed and proved by mathematical induction according to the location relationship between the starting node and the end node of the path.(2)If a structure of the node degree is less than or equal to 2,then the structure does not exist the Hamiltonian and prove that the network structure of the minimum cut set and number less than or equal to 2,the network structure has not Hamiltonian,These two theorems analyze the condition that there is no Hamiltonian from the low-level nodes and high-level structures,finally analyzes the FiConn,ExCCC,BCube,DCell Hamiltonian of the network structure.(3)The Hamiltonian path search algorithm based on BCube and DCell is proposed,According to the depth-first principle,the Hamiltonian path of BCube and DCell can be established.Based on the existing network topology and Hamiltonian analysis,this paper proposes theorems that satisfy certain conditions of existence and non-existence of Hamiltonian,studies and analyzes the network structure BCube to find the Hamiltonian path,and provides the basis for the research on the Hamiltonian of data center network structure.