According to the researches on theoretic basis in part Ⅰ of the paper, the spanning tree algorithms solving the maximum independent set both in even network and in odd network have been developed in this part, part ...According to the researches on theoretic basis in part Ⅰ of the paper, the spanning tree algorithms solving the maximum independent set both in even network and in odd network have been developed in this part, part Ⅱ of the paper. The algorithms transform first the general network into the pair sets network, and then decompose the pair sets network into a series of pair subsets by use of the characteristic of maximum flow passing through the pair sets network. As for the even network, the algorithm requires only one time of transformation and decomposition, the maximum independent set can be gained without any iteration processes, and the time complexity of the algorithm is within the bound of O(V3). However, as for the odd network, the algorithm consists of two stages. In the first stage, the general odd network is transformed and decomposed into the pseudo-negative envelope graphs and generalized reverse pseudo-negative envelope graphs alternately distributed at first; then the algorithm turns to the second stage, searching for the negative envelope graphs within the pseudo-negative envelope graphs only. Each time as a negative envelope graph has been found, renew the pair sets network by iteration at once, and then turn back to the first stage. So both stages form a circulation process up to the optimum. Two available methods, the adjusting search and the picking-off search are specially developed to deal with the problems resulted from the odd network. Both of them link up with each other harmoniously and are embedded together in the algorithm. Analysis and study indicate that the time complexity of this algorithm is within the bound of O(V5).展开更多
The structure and characteristics of a connected network are analyzed, and a special kind of sub-network, which can optimize the iteration processes, is discovered. Then, the sufficient and necessary conditions for o...The structure and characteristics of a connected network are analyzed, and a special kind of sub-network, which can optimize the iteration processes, is discovered. Then, the sufficient and necessary conditions for obtaining the maximum independent set are deduced. It is found that the neighborhood of this sub-network possesses the similar characters, but both can never be allowed incorporated together. Particularly, it is identified that the network can be divided into two parts by a certain style, and then both of them can be transformed into a pair sets network, where the special sub-networks and their neighborhoods appear alternately distributed throughout the entire pair sets network. By use of this characteristic, the network decomposed enough without losing any solutions is obtained. All of these above will be able to make well ready for developing a much better algorithm with polynomial time bound for an odd network in the the application research part of this subject.展开更多
In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously pe...In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously perform the local computation,which calls for heavy computational and communication costs.Moreover,in many real-world networks,such as those with straggling nodes,the homogeneous manner may result in serious delay or even failure.To this end,we propose active network decomposition algorithms to select non-straggling nodes(normal nodes)that perform the main computation and communication across the network.To accommodate the decomposition in different kinds of networks,two different approaches are developed,one is centralized decomposition that leverages the adjacency of the network and the other is distributed decomposition that employs the indicator message transmission between neighboring nodes,which constitutes the main contribution of this paper.By incorporating the active decomposition scheme,a distributed Newton method is employed to solve the least squares problem in GSP,where the Hessian inverse is approximately evaluated by patching a series of inverses of local Hessian matrices each of which is governed by one normal node.The proposed algorithm inherits the fast convergence of the second-order algorithms while maintains low computational and communication cost.Numerical examples demonstrate the effectiveness of the proposed algorithm.展开更多
The detection of error and its correction is an important area of mathematics that is vastly constructed in all communication systems.Furthermore,combinatorial design theory has several applications like detecting or ...The detection of error and its correction is an important area of mathematics that is vastly constructed in all communication systems.Furthermore,combinatorial design theory has several applications like detecting or correcting errors in communication systems.Network(graph)designs(GDs)are introduced as a generalization of the symmetric balanced incomplete block designs(BIBDs)that are utilized directly in the above mentioned application.The networks(graphs)have been represented by vectors whose entries are the labels of the vertices related to the lengths of edges linked to it.Here,a general method is proposed and applied to construct new networks designs.This method of networks representation has simplified the method of constructing the network designs.In this paper,a novel representation of networks is introduced and used as a technique of constructing the group generated network designs of the complete bipartite networks and certain circulants.A technique of constructing the group generated network designs of the circulants is given with group generated graph designs(GDs)of certain circulants.In addition,the GDs are transformed into an incidence matrices,the rows and the columns of these matrices can be both viewed as a binary nonlinear code.A novel coding error detection and correction application is proposed and examined.展开更多
The tremendous performance gain of heterogeneous networks(Het Nets) is at the cost of complicated resource allocation. Considering information security, the resource allocation for Het Nets becomes much more challengi...The tremendous performance gain of heterogeneous networks(Het Nets) is at the cost of complicated resource allocation. Considering information security, the resource allocation for Het Nets becomes much more challenging and this is the focus of this paper. In this paper, the eavesdropper is hidden from the macro base stations. To relax the unpractical assumption on the channel state information on eavesdropper, a localization based algorithm is first given. Then a joint resource allocation algorithm is proposed in our work, which simultaneously considers physical layer security, cross-tier interference and joint optimization of power and subcarriers under fairness requirements. It is revealed in our work that the considered optimization problem can be efficiently solved relying on convex optimization theory and the Lagrangian dual decomposition method is exploited to solve the considered problem effectively. Moreover, in each iteration the closed-form optimal resource allocation solutions can be obtained based on the Karush-Kuhn-Tucker(KKT) conditions. Finally, the simulation results are given to show the performance advantages of the proposed algorithm.展开更多
Cache-enabled small cell networks have been regarded as a promising approach for network operators to cope with the explosive data traffic growth in future 5 G networks. However, the user association and resource allo...Cache-enabled small cell networks have been regarded as a promising approach for network operators to cope with the explosive data traffic growth in future 5 G networks. However, the user association and resource allocation mechanism has not been thoroughly studied under given content placement situation. In this paper, we formulate the joint optimization problem of user association and resource allocation as a mixed integer nonlinear programming(MINLP) problem aiming at deriving a balance between the total utility of data rates and the total data rates retrieved from caches. To solve this problem, we propose a distributed relaxing-rounding method. Simulation results demonstrate that the distributed relaxing-rounding method outperforms traditional max-SINR method and range-expansion method in terms of both total utility of data rates and total data rates retrieved from caches in practical scenarios. In addition, effects of storage and backhaul capacities on the performance are also studied.展开更多
Previous studies revealed that the error of pole coordinate prediction will significantly increase for a prediction period longer than 100 days, and this is mainly caused by short period oscillations. Empirical mode d...Previous studies revealed that the error of pole coordinate prediction will significantly increase for a prediction period longer than 100 days, and this is mainly caused by short period oscillations. Empirical mode decomposition （EMD）, which is increasingly popular and has advantages over classical wavelet decomposition, can be used to remove short period variations from observed time series of pole co- ordinates. A hybrid model combing EMD and extreme learning machine （ELM）, where high frequency signals are removed and processed time series is then modeled and predicted, is summarized in this paper. The prediction performance of the hybrid model is compared with that of the ELM-only method created from original time series. The results show that the proposed hybrid model outperforms the pure ELM method for both short-term and long-term prediction of pole coordinates. The improvement of prediction accuracy up to 360 days in the future is found to be 24.91% and 26.79% on average in terms of mean absolute error （MAE） for the xp and yp components of pole coordinates, respectively.展开更多
The novel information criterion （NIC） algorithm can find the principal subspace quickly, but it is not an actual principal component analysis （PCA） algorithm and hence it cannot find the orthonormal eigen-space wh...The novel information criterion （NIC） algorithm can find the principal subspace quickly, but it is not an actual principal component analysis （PCA） algorithm and hence it cannot find the orthonormal eigen-space which corresponds to the principal component of input vector. This defect limits its application in practice. By weighting the neural network＇s output of NIC, a modified novel information criterion （MNIC） algorithm is presented. MNIC extractes the principal components and corresponding eigenvectors in a parallel online learning program, and overcomes the NIC＇s defect. It is proved to have a single global optimum and nonquadratic convergence rate, which is superior to the conventional PCA online algorithms such as Oja and LMSER. The relationship among Oja, LMSER and MNIC is exhibited. Simulations show that MNIC could converge to the optimum fast. The validity of MNIC is proved.展开更多
文摘According to the researches on theoretic basis in part Ⅰ of the paper, the spanning tree algorithms solving the maximum independent set both in even network and in odd network have been developed in this part, part Ⅱ of the paper. The algorithms transform first the general network into the pair sets network, and then decompose the pair sets network into a series of pair subsets by use of the characteristic of maximum flow passing through the pair sets network. As for the even network, the algorithm requires only one time of transformation and decomposition, the maximum independent set can be gained without any iteration processes, and the time complexity of the algorithm is within the bound of O(V3). However, as for the odd network, the algorithm consists of two stages. In the first stage, the general odd network is transformed and decomposed into the pseudo-negative envelope graphs and generalized reverse pseudo-negative envelope graphs alternately distributed at first; then the algorithm turns to the second stage, searching for the negative envelope graphs within the pseudo-negative envelope graphs only. Each time as a negative envelope graph has been found, renew the pair sets network by iteration at once, and then turn back to the first stage. So both stages form a circulation process up to the optimum. Two available methods, the adjusting search and the picking-off search are specially developed to deal with the problems resulted from the odd network. Both of them link up with each other harmoniously and are embedded together in the algorithm. Analysis and study indicate that the time complexity of this algorithm is within the bound of O(V5).
文摘The structure and characteristics of a connected network are analyzed, and a special kind of sub-network, which can optimize the iteration processes, is discovered. Then, the sufficient and necessary conditions for obtaining the maximum independent set are deduced. It is found that the neighborhood of this sub-network possesses the similar characters, but both can never be allowed incorporated together. Particularly, it is identified that the network can be divided into two parts by a certain style, and then both of them can be transformed into a pair sets network, where the special sub-networks and their neighborhoods appear alternately distributed throughout the entire pair sets network. By use of this characteristic, the network decomposed enough without losing any solutions is obtained. All of these above will be able to make well ready for developing a much better algorithm with polynomial time bound for an odd network in the the application research part of this subject.
基金supported by National Natural Science Foundation of China(Grant No.61761011)Natural Science Foundation of Guangxi(Grant No.2020GXNSFBA297078).
文摘In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously perform the local computation,which calls for heavy computational and communication costs.Moreover,in many real-world networks,such as those with straggling nodes,the homogeneous manner may result in serious delay or even failure.To this end,we propose active network decomposition algorithms to select non-straggling nodes(normal nodes)that perform the main computation and communication across the network.To accommodate the decomposition in different kinds of networks,two different approaches are developed,one is centralized decomposition that leverages the adjacency of the network and the other is distributed decomposition that employs the indicator message transmission between neighboring nodes,which constitutes the main contribution of this paper.By incorporating the active decomposition scheme,a distributed Newton method is employed to solve the least squares problem in GSP,where the Hessian inverse is approximately evaluated by patching a series of inverses of local Hessian matrices each of which is governed by one normal node.The proposed algorithm inherits the fast convergence of the second-order algorithms while maintains low computational and communication cost.Numerical examples demonstrate the effectiveness of the proposed algorithm.
基金support from Taif University Researchers Supporting Project Number(TURSP-2020/031),Taif University,Taif,Saudi Arabia.
文摘The detection of error and its correction is an important area of mathematics that is vastly constructed in all communication systems.Furthermore,combinatorial design theory has several applications like detecting or correcting errors in communication systems.Network(graph)designs(GDs)are introduced as a generalization of the symmetric balanced incomplete block designs(BIBDs)that are utilized directly in the above mentioned application.The networks(graphs)have been represented by vectors whose entries are the labels of the vertices related to the lengths of edges linked to it.Here,a general method is proposed and applied to construct new networks designs.This method of networks representation has simplified the method of constructing the network designs.In this paper,a novel representation of networks is introduced and used as a technique of constructing the group generated network designs of the complete bipartite networks and certain circulants.A technique of constructing the group generated network designs of the circulants is given with group generated graph designs(GDs)of certain circulants.In addition,the GDs are transformed into an incidence matrices,the rows and the columns of these matrices can be both viewed as a binary nonlinear code.A novel coding error detection and correction application is proposed and examined.
基金supported by the National Natural Science Foundation of China under Grant No.61371075the 863 project SS2015AA011306
文摘The tremendous performance gain of heterogeneous networks(Het Nets) is at the cost of complicated resource allocation. Considering information security, the resource allocation for Het Nets becomes much more challenging and this is the focus of this paper. In this paper, the eavesdropper is hidden from the macro base stations. To relax the unpractical assumption on the channel state information on eavesdropper, a localization based algorithm is first given. Then a joint resource allocation algorithm is proposed in our work, which simultaneously considers physical layer security, cross-tier interference and joint optimization of power and subcarriers under fairness requirements. It is revealed in our work that the considered optimization problem can be efficiently solved relying on convex optimization theory and the Lagrangian dual decomposition method is exploited to solve the considered problem effectively. Moreover, in each iteration the closed-form optimal resource allocation solutions can be obtained based on the Karush-Kuhn-Tucker(KKT) conditions. Finally, the simulation results are given to show the performance advantages of the proposed algorithm.
基金supported by National Natural Science Foundation of China under Grants No. 61371087 and 61531013The Research Fund of Ministry of Education-China Mobile (MCM20150102)
文摘Cache-enabled small cell networks have been regarded as a promising approach for network operators to cope with the explosive data traffic growth in future 5 G networks. However, the user association and resource allocation mechanism has not been thoroughly studied under given content placement situation. In this paper, we formulate the joint optimization problem of user association and resource allocation as a mixed integer nonlinear programming(MINLP) problem aiming at deriving a balance between the total utility of data rates and the total data rates retrieved from caches. To solve this problem, we propose a distributed relaxing-rounding method. Simulation results demonstrate that the distributed relaxing-rounding method outperforms traditional max-SINR method and range-expansion method in terms of both total utility of data rates and total data rates retrieved from caches in practical scenarios. In addition, effects of storage and backhaul capacities on the performance are also studied.
基金supported by Chinese Academy of Sciences(No.201491)“Light of West China” Program(201491)
文摘Previous studies revealed that the error of pole coordinate prediction will significantly increase for a prediction period longer than 100 days, and this is mainly caused by short period oscillations. Empirical mode decomposition （EMD）, which is increasingly popular and has advantages over classical wavelet decomposition, can be used to remove short period variations from observed time series of pole co- ordinates. A hybrid model combing EMD and extreme learning machine （ELM）, where high frequency signals are removed and processed time series is then modeled and predicted, is summarized in this paper. The prediction performance of the hybrid model is compared with that of the ELM-only method created from original time series. The results show that the proposed hybrid model outperforms the pure ELM method for both short-term and long-term prediction of pole coordinates. The improvement of prediction accuracy up to 360 days in the future is found to be 24.91% and 26.79% on average in terms of mean absolute error （MAE） for the xp and yp components of pole coordinates, respectively.
文摘The novel information criterion （NIC） algorithm can find the principal subspace quickly, but it is not an actual principal component analysis （PCA） algorithm and hence it cannot find the orthonormal eigen-space which corresponds to the principal component of input vector. This defect limits its application in practice. By weighting the neural network＇s output of NIC, a modified novel information criterion （MNIC） algorithm is presented. MNIC extractes the principal components and corresponding eigenvectors in a parallel online learning program, and overcomes the NIC＇s defect. It is proved to have a single global optimum and nonquadratic convergence rate, which is superior to the conventional PCA online algorithms such as Oja and LMSER. The relationship among Oja, LMSER and MNIC is exhibited. Simulations show that MNIC could converge to the optimum fast. The validity of MNIC is proved.
