The hybrid routing protocol has received more attention recently than the proactive and the reactive, especially for large-scale and highly dynamic connection,in mobile ad hoc network. A crucial reason is that zone-la...The hybrid routing protocol has received more attention recently than the proactive and the reactive, especially for large-scale and highly dynamic connection,in mobile ad hoc network. A crucial reason is that zone-layered is being utilized in the complex systems.A hybrid routing algorithm which is layered zone based on adjacency connection(LZBAC) is put forward under the background of a few members in network with steady position and link. The algorithm modifies storage structure of nodes and improves routing mechanism. The theoretical analysis and simulation testing testify that the algorithm costs shorter time of route finding and less delay than others.展开更多
Based on traffic engineering, the network topology is described with network graph. An algorithm for the derivation of data communication capability in network links and the analysis of connectivity performance betwee...Based on traffic engineering, the network topology is described with network graph. An algorithm for the derivation of data communication capability in network links and the analysis of connectivity performance between node pairs is given through standardized transformation of the original descriptive matrix for the link performance, and resolution of transitive closure for adjacent-incident matrix of network in view of randomness of network events, which provides a feasible way for analysis and improvement of network performance.展开更多
Given an alphabet ∑ and a finite minimal set B of forbidden words,a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any str...Given an alphabet ∑ and a finite minimal set B of forbidden words,a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any string in B as their substrings.From the fact that a string in the language is equivalent to a path in the corresponding graph,we have obtained a polynomial time algorithm by modifying the power of the adjacency matrix in the graph.展开更多
This paper constructs a new spectrum of networks by means of the matrix of link-state ofthe network,which can reveal the characteristics of the correlation between the degrees of the network.Also,the computation of th...This paper constructs a new spectrum of networks by means of the matrix of link-state ofthe network,which can reveal the characteristics of the correlation between the degrees of the network.Also,the computation of this spectrum of networks is usually more feasible and more efficient due tothe much lower order of its matrix of link-state than its adjacent matrix in practice.Some estimatesfor the bounds of the key eigenvalues in the spectrum are obtained,the corresponding inequalities arepresented and proved.For the sake of its application,the authors define spectrum of networks in twoways,and all theorems are given in parallel for both kinds of definition.In addition,the authors finda symmetry in the spectrum,which is relative to the characteristic of structure of its network to someextent.展开更多
Let A be a j x d (0,1) matrix. It is known that if j = 2k - 1 is odd, then det(AAT) ≤ (j+1)((j+1)d/4j)j; if j is even, then det(AAT) ≤ (j+1)((j+2)d/4(j+1))j. A is called a regular D-optimal matrix if it satisfies th...Let A be a j x d (0,1) matrix. It is known that if j = 2k - 1 is odd, then det(AAT) ≤ (j+1)((j+1)d/4j)j; if j is even, then det(AAT) ≤ (j+1)((j+2)d/4(j+1))j. A is called a regular D-optimal matrix if it satisfies the equality of the above bounds. In this note, it is proved that if j = 2k - 1 is odd, then A is a regular D-optimal matrix if and only if A is the adjacent matrix of a (2k - 1, k, (j + l)d/4j)-BIBD; if j = 2k is even, then A is a regular D-optimal matrix if and only if A can be obtained from the adjacent matrix B of a (2k + 1,k + 1,(j + 2)d/4(j +1))-BIBD by deleting any one row from B. Three 21 x 42 regular D-optimal matrices, which were unknown in [11], are also provided.展开更多
Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti an...Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui ： i = 1, 2 , m}. Let κ = ec＋1. Forj = 1,2,...,k- 1, let δij = max{dv ： dist（v, ui） = j,v ∈ Ti}, δj = max{δij ： i = 1, 2,..., m}, δ0 = max{dui ： ui ∈ V（Cm）}. Then λ1（G）≤max{max 2≤j≤k-2 （√δj-1-1＋√δj-1）,2＋√δ0-2,√δ0-2＋√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 （G） is the largest eigenvalue of the adjacency matrix of G.展开更多
基金This work was supported in part by Research fund from Educational Committee of China (No104086)
文摘The hybrid routing protocol has received more attention recently than the proactive and the reactive, especially for large-scale and highly dynamic connection,in mobile ad hoc network. A crucial reason is that zone-layered is being utilized in the complex systems.A hybrid routing algorithm which is layered zone based on adjacency connection(LZBAC) is put forward under the background of a few members in network with steady position and link. The algorithm modifies storage structure of nodes and improves routing mechanism. The theoretical analysis and simulation testing testify that the algorithm costs shorter time of route finding and less delay than others.
文摘Based on traffic engineering, the network topology is described with network graph. An algorithm for the derivation of data communication capability in network links and the analysis of connectivity performance between node pairs is given through standardized transformation of the original descriptive matrix for the link performance, and resolution of transitive closure for adjacent-incident matrix of network in view of randomness of network events, which provides a feasible way for analysis and improvement of network performance.
基金This research is supported by the National Natural Science Foundation of China (No. 10271103) Natural Science Foundation of Yunnan Province(No. 2003F0015M).
文摘Given an alphabet ∑ and a finite minimal set B of forbidden words,a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any string in B as their substrings.From the fact that a string in the language is equivalent to a path in the corresponding graph,we have obtained a polynomial time algorithm by modifying the power of the adjacency matrix in the graph.
基金supported by the Key Project for Fundamental Research of STCSM under Grant No. 06JC14057
文摘This paper constructs a new spectrum of networks by means of the matrix of link-state ofthe network,which can reveal the characteristics of the correlation between the degrees of the network.Also,the computation of this spectrum of networks is usually more feasible and more efficient due tothe much lower order of its matrix of link-state than its adjacent matrix in practice.Some estimatesfor the bounds of the key eigenvalues in the spectrum are obtained,the corresponding inequalities arepresented and proved.For the sake of its application,the authors define spectrum of networks in twoways,and all theorems are given in parallel for both kinds of definition.In addition,the authors finda symmetry in the spectrum,which is relative to the characteristic of structure of its network to someextent.
基金Project supported by the Science Foundation of China for Postdoctors (No.5(2001)).
文摘Let A be a j x d (0,1) matrix. It is known that if j = 2k - 1 is odd, then det(AAT) ≤ (j+1)((j+1)d/4j)j; if j is even, then det(AAT) ≤ (j+1)((j+2)d/4(j+1))j. A is called a regular D-optimal matrix if it satisfies the equality of the above bounds. In this note, it is proved that if j = 2k - 1 is odd, then A is a regular D-optimal matrix if and only if A is the adjacent matrix of a (2k - 1, k, (j + l)d/4j)-BIBD; if j = 2k is even, then A is a regular D-optimal matrix if and only if A can be obtained from the adjacent matrix B of a (2k + 1,k + 1,(j + 2)d/4(j +1))-BIBD by deleting any one row from B. Three 21 x 42 regular D-optimal matrices, which were unknown in [11], are also provided.
基金Foundation item： the National Natural Science Foundation of China （No. 10861009）.
文摘Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui ： i = 1, 2 , m}. Let κ = ec＋1. Forj = 1,2,...,k- 1, let δij = max{dv ： dist（v, ui） = j,v ∈ Ti}, δj = max{δij ： i = 1, 2,..., m}, δ0 = max{dui ： ui ∈ V（Cm）}. Then λ1（G）≤max{max 2≤j≤k-2 （√δj-1-1＋√δj-1）,2＋√δ0-2,√δ0-2＋√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 （G） is the largest eigenvalue of the adjacency matrix of G.
