To guarantee the safety of railway operations,the swift detection of rail surface defects becomes imperative.Traditional methods of manual inspection and conventional nondestructive testing prove inefficient,especiall...To guarantee the safety of railway operations,the swift detection of rail surface defects becomes imperative.Traditional methods of manual inspection and conventional nondestructive testing prove inefficient,especially when scaling to extensive railway networks.Moreover,the unpredictable and intricate nature of defect edge shapes further complicates detection efforts.Addressing these challenges,this paper introduces an enhanced Unified Perceptual Parsing for Scene Understanding Network(UPerNet)tailored for rail surface defect detection.Notably,the Swin Transformer Tiny version(Swin-T)network,underpinned by the Transformer architecture,is employed for adept feature extraction.This approach capitalizes on the global information present in the image and sidesteps the issue of inductive preference.The model’s efficiency is further amplified by the windowbased self-attention,which minimizes the model’s parameter count.We implement the cross-GPU synchronized batch normalization(SyncBN)for gradient optimization and integrate the Lovász-hinge loss function to leverage pixel dependency relationships.Experimental evaluations underscore the efficacy of our improved UPerNet,with results demonstrating Pixel Accuracy(PA)scores of 91.39%and 93.35%,Intersection over Union(IoU)values of 83.69%and 87.58%,Dice Coefficients of 91.12%and 93.38%,and Precision metrics of 90.85%and 93.41%across two distinct datasets.An increment in detection accuracy was discernible.For further practical applicability,we deploy semantic segmentation of rail surface defects,leveraging connected component processing techniques to distinguish varied defects within the same frame.By computing the actual defect length and area,our deep learning methodology presents results that offer intuitive insights for railway maintenance professionals.展开更多
A fast label-equivalence-based connected components labeling algorithm is proposed in this paper.It is a combination of two existing efficient methods,which are pivotal operations in two-pass connected components labe...A fast label-equivalence-based connected components labeling algorithm is proposed in this paper.It is a combination of two existing efficient methods,which are pivotal operations in two-pass connected components labeling algorithms.One is a fast pixel scan method,and the other is an array-based Union-Find data structure.The scan procedure assigns each foreground pixel a provisional label according to the location of the pixel.That is to say,it labels the foreground pixels following background pixels and foreground pixels in different ways,which greatly reduces the number of neighbor pixel checks.The array-based Union-Find data structure resolves the label equivalences between provisional labels by using only a single array with path compression,and it improves the efficiency of the resolving procedure which is very time-consuming in general label-equivalence-based algorithms.The experiments on various types of images with different sizes show that the proposed algorithm is superior to other labeling approaches for huge images containing many big connected components.展开更多
An Intelligent Transportation System (ITS) is a new system developed for the betterment of user in traffic and transport management domain area for smart and safe driving. ITS subsystems are Emergency vehicle notifica...An Intelligent Transportation System (ITS) is a new system developed for the betterment of user in traffic and transport management domain area for smart and safe driving. ITS subsystems are Emergency vehicle notification systems, Automatic road enforcement, Collision avoidance systems, Automatic parking, Map database management, etc. Advance Driver Assists System (ADAS) belongs to ITS which provides alert or warning or information to the user during driving. The proposed method uses Gaussian filtering and Median filtering to remove noise in the image. Subsequently image subtraction is achieved by subtracting Median filtered image from Gaussian filtered image. The resultant image is converted to binary image and the regions are analyzed using connected component approach. The prior work on speed bump detection is achieved using sensors which are failed to detect speed bumps that are constructed with small height and the detection rate is affected due to erroneous identification. And the smartphone and accelerometer methodologies are not perfectly suitable for real time scenario due to GPS error, network overload, real-time delay, accuracy and battery running out. The proposed system goes very well for the roads which are constructed with proper painting irrespective of their dimension.展开更多
Let g and h be two transcendental entire functions. Suppose that the Fatou set F(goh) contains multiply connected components. In this article, we will consider the growth of the functions g and h.
Let A be a basic connected finite dimensional associative algebra over an algebraically closed field k and G be a cyclic group.There is a quiver QGwith relationsρG such that the skew group algebras A[G]is Morita equi...Let A be a basic connected finite dimensional associative algebra over an algebraically closed field k and G be a cyclic group.There is a quiver QGwith relationsρG such that the skew group algebras A[G]is Morita equivalent to the quotient algebra of path algebra kQGmodulo ideal(ρG).Generally,the quiver QGis not connected.In this paper we develop a method to determine the number of connect components of QG.Meanwhile,we introduce the notion of weight for underlying quiver of A such that A is G-graded and determine the connect components of smash product A#kG*.展开更多
Brain tumor significantly impacts the quality of life and changes everything for a patient and their loved ones.Diagnosing a brain tumor usually begins with magnetic resonance imaging(MRI).The manual brain tumor diagn...Brain tumor significantly impacts the quality of life and changes everything for a patient and their loved ones.Diagnosing a brain tumor usually begins with magnetic resonance imaging(MRI).The manual brain tumor diagnosis from the MRO images always requires an expert radiologist.However,this process is time-consuming and costly.Therefore,a computerized technique is required for brain tumor detection in MRI images.Using the MRI,a novel mechanism of the three-dimensional(3D)Kronecker convolution feature pyramid(KCFP)is used to segment brain tumors,resolving the pixel loss and weak processing of multi-scale lesions.A single dilation rate was replaced with the 3D Kronecker convolution,while local feature learning was performed using the 3D Feature Selection(3DFSC).A 3D KCFP was added at the end of 3DFSC to resolve weak processing of multi-scale lesions,yielding efficient segmentation of brain tumors of different sizes.A 3D connected component analysis with a global threshold was used as a post-processing technique.The standard Multimodal Brain Tumor Segmentation 2020 dataset was used for model validation.Our 3D KCFP model performed exceptionally well compared to other benchmark schemes with a dice similarity coefficient of 0.90,0.80,and 0.84 for the whole tumor,enhancing tumor,and tumor core,respectively.Overall,the proposed model was efficient in brain tumor segmentation,which may facilitate medical practitioners for an appropriate diagnosis for future treatment planning.展开更多
The commuting graph of an arbitrary ring R, denoted by Г(R), is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we inv...The commuting graph of an arbitrary ring R, denoted by Г(R), is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity and the diameter of Г(ZnS3). We show that Г(ZnS3) is connected if and only if n is not a prime number. If Г(ZnS3) is connected then diam(Г(ZnS3)) = 3, while ifГ(ZnS3) is disconnected then every connected component of Г(ZnS3) must be a complete graph with same size, and we completely determine the vertice set of every connected component.展开更多
Different methods for revising propositional knowledge base have been proposed recently by several researchers, but all methods are intractable in the general case. For practical application, this paper presents a rev...Different methods for revising propositional knowledge base have been proposed recently by several researchers, but all methods are intractable in the general case. For practical application, this paper presents a revision method in special case, and gives a corresponding polynomial algorithm as well as its parallel version on CREW PRAM.展开更多
Given a digraph D =(V, A), the competition graph G of D, denoted by C(D), has the same set of vertices as D and an edge between vertices x and y if and only if N;(x)∩N;(y)≠Ф. In this paper, we investigate t...Given a digraph D =(V, A), the competition graph G of D, denoted by C(D), has the same set of vertices as D and an edge between vertices x and y if and only if N;(x)∩N;(y)≠Ф. In this paper, we investigate the competition graphs of round digraphs and give a necessary and sufficient condition for these graphs to be hamiltonian.展开更多
Let B(R^n) be the set of all n x n real matrices, Sr the set of all matrices with rank r, 0 ≤ r ≤ n, and Sr^# the number of arcwise connected components of Sr. It is well-known that Sn =GL(R^n) is a Lie group an...Let B(R^n) be the set of all n x n real matrices, Sr the set of all matrices with rank r, 0 ≤ r ≤ n, and Sr^# the number of arcwise connected components of Sr. It is well-known that Sn =GL(R^n) is a Lie group and also a smooth hypersurface in B(R^n) with the dimension n × n.展开更多
Let G be a finite group with order g and S be a subring of the algebraic number field which contains the integral extension over Z generated by a g-th primitive root co of unity, and R(G) be the character ring of G....Let G be a finite group with order g and S be a subring of the algebraic number field which contains the integral extension over Z generated by a g-th primitive root co of unity, and R(G) be the character ring of G. The prime spectrum of the commutative ring S×Z R(G) iv denoted by Spec(S×Z R(G)) and set π={p|p is a rational prime number such that p^-1 S}. We prove that when G is a regroup, a π'-group, or a finite Abelian group, the number of the connetted components of Spec( S×Z R (G) ) coincides with the number of the π-regular classes in G,展开更多
The identification of objects in binary images is a fundamental task in image analysis and pattern recognition tasks. The Euler number of a binary image is an important topological measure which is used as a feature i...The identification of objects in binary images is a fundamental task in image analysis and pattern recognition tasks. The Euler number of a binary image is an important topological measure which is used as a feature in image analysis. In this paper, a very fast algorithm for the detection and localization of the objects and the computation of the Euler number of a binary image is proposed. The proposed algorithm operates in one scan of the image and is based on the Image Block Representation (IBR) scheme. The proposed algorithm is more efficient than conventional pixel based algorithms in terms of execution speed and representation of the extracted information.展开更多
Direct current(DC)bus voltage stability is essential for the stable and reliable operation of a DC system.If an oscillation source can be quickly and accurately localized,the oscillation can be adequately eliminated.W...Direct current(DC)bus voltage stability is essential for the stable and reliable operation of a DC system.If an oscillation source can be quickly and accurately localized,the oscillation can be adequately eliminated.We propose a method based on the power spectral density for identifying the voltage oscillation source.Specifically,a DC distribution network model combined with the component connection method is developed,and the network is separated into multiple power modules.Compared with a conventional method,the proposed method does not require determining the model parameters of the entire power grid,which is typically challenging.Furthermore,combined with a novel judgment index,the oscillation source can be identified more intuitively and clearly to enhance the applicability to real power grids.The performance of the proposed method has been evaluated using the MATLAB/Simulink software and PLECS RT Box experimental platform.The simulation and experimental results verify that the proposed method can accurately identify oscillation sources in a DC distribution network.展开更多
A graph is called a proper refinement of a star graph if it is a refinement of a star graph, but it is neither a star graph nor a complete graph. For a refinement of a star graph G with center c, let G* be the subgra...A graph is called a proper refinement of a star graph if it is a refinement of a star graph, but it is neither a star graph nor a complete graph. For a refinement of a star graph G with center c, let G* be the subgraph of G induced on the vertex set V(G) / {c or end vertices adjacent to c}. In this paper, we study the isomorphic classification of some finite commutative local rings R by investigating their zero-divisor graphs G=Г(R), which is a proper refinement of a star graph with exactly one center c. We determine all finite commutative local rings R such that G* has at least two connected components. We prove that the diameter of the induced graph G* is two if Z(R)2 ≠{0}, Z(R)3 = {0} and Gc is connected. We determine the structure of R which has two distinct nonadjacent vertices a, fl C Z(R)*/{c} such that the ideal [N(a)N(β)]{0} is generated by only one element of Z(R)*/{c}. We also completely determine the correspondence between commutative rings and finite complete graphs Kn with some end vertices adjacent to a single vertex of Kn.展开更多
In this paper,a sequential algorithm computing the all vertex pair distance matrix D and the path matrix Pis given.On a PRAM EREW model with p,1≤p≤n^2,processors,a parallel version of the sequential algorithm is sho...In this paper,a sequential algorithm computing the all vertex pair distance matrix D and the path matrix Pis given.On a PRAM EREW model with p,1≤p≤n^2,processors,a parallel version of the sequential algorithm is shown.This method can also be used to get a parallel algorithm to compute transitive closure arrayof an undirected graph.The time complexify of the parallel algorithm is O(n^3/p).If D,P andare known,it is shown that the problems to find all connected components, to compute the diameter of an undirected graph,to determine the center of a directed graph and to search for a directed cycle with the minimum(maximum)length in a directed graph can all be solved in O(n^2/p^+ logp)time.展开更多
It is a common practice to simulate some historical or test systems to validate the efficiency of new methods or concepts. However, there are only a small number of existing power system test cases, and validation and...It is a common practice to simulate some historical or test systems to validate the efficiency of new methods or concepts. However, there are only a small number of existing power system test cases, and validation and evaluation results, obtained using such a limited number of test cases, may not be deemed sufficient or convincing. In order to provide more available test cases, a new random graph generation algorithm, named ‘‘dualstage constructed random graph’’ algorithm, is proposed to effectively model the power grid topology. The algorithm generates a spanning tree to guarantee the connectivity of random graphs and is capable of controlling the number of lines precisely. No matter how much the average degree is,whether sparse or not, random graphs can be quickly formed to satisfy the requirements. An approach is developed to generate random graphs with prescribed numbers of connected components, in order to simulate the power grid topology under fault conditions. Our experimental study on several realistic power grid topologies proves that the proposed algorithm can quickly generate a large number of random graphs with the topology characteristics of real-world power grid.展开更多
The k-component edgeconnectivity cλk(G)of anon-completegraph G is themini mum number of edges whose deletion results in a graph with at least k components In this paper,we extend some results by Guo et al.(Appl Math ...The k-component edgeconnectivity cλk(G)of anon-completegraph G is themini mum number of edges whose deletion results in a graph with at least k components In this paper,we extend some results by Guo et al.(Appl Math Comput 334:401-406,2018)by determining the component edge connectivity of the locally twisted cubes LTQn,i.e.,cλk+1(LTQn)=kn-exk/2for 1≤2[n/2],n≥7,where exk=∑si=0ti2ti+∑si=02·i·2ti,and k is a positive integer with decomposition k=∑si=02ti such that to="log2k"and ti="log2(k-∑i-1 r=02tr)"for i≥1.As a by-product,we characterize the corresponding optimal solutions.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant No.62066024)Gansu Province Higher Education Industry Support Plan(2021CYZC34)Lanzhou Talent Innovation and Entrepreneurship Project(2021-RC-27,2021-RC-45).
文摘To guarantee the safety of railway operations,the swift detection of rail surface defects becomes imperative.Traditional methods of manual inspection and conventional nondestructive testing prove inefficient,especially when scaling to extensive railway networks.Moreover,the unpredictable and intricate nature of defect edge shapes further complicates detection efforts.Addressing these challenges,this paper introduces an enhanced Unified Perceptual Parsing for Scene Understanding Network(UPerNet)tailored for rail surface defect detection.Notably,the Swin Transformer Tiny version(Swin-T)network,underpinned by the Transformer architecture,is employed for adept feature extraction.This approach capitalizes on the global information present in the image and sidesteps the issue of inductive preference.The model’s efficiency is further amplified by the windowbased self-attention,which minimizes the model’s parameter count.We implement the cross-GPU synchronized batch normalization(SyncBN)for gradient optimization and integrate the Lovász-hinge loss function to leverage pixel dependency relationships.Experimental evaluations underscore the efficacy of our improved UPerNet,with results demonstrating Pixel Accuracy(PA)scores of 91.39%and 93.35%,Intersection over Union(IoU)values of 83.69%and 87.58%,Dice Coefficients of 91.12%and 93.38%,and Precision metrics of 90.85%and 93.41%across two distinct datasets.An increment in detection accuracy was discernible.For further practical applicability,we deploy semantic segmentation of rail surface defects,leveraging connected component processing techniques to distinguish varied defects within the same frame.By computing the actual defect length and area,our deep learning methodology presents results that offer intuitive insights for railway maintenance professionals.
基金Sponsored by the National Natural Science Foundation of China (Grant No. 81071219)
文摘A fast label-equivalence-based connected components labeling algorithm is proposed in this paper.It is a combination of two existing efficient methods,which are pivotal operations in two-pass connected components labeling algorithms.One is a fast pixel scan method,and the other is an array-based Union-Find data structure.The scan procedure assigns each foreground pixel a provisional label according to the location of the pixel.That is to say,it labels the foreground pixels following background pixels and foreground pixels in different ways,which greatly reduces the number of neighbor pixel checks.The array-based Union-Find data structure resolves the label equivalences between provisional labels by using only a single array with path compression,and it improves the efficiency of the resolving procedure which is very time-consuming in general label-equivalence-based algorithms.The experiments on various types of images with different sizes show that the proposed algorithm is superior to other labeling approaches for huge images containing many big connected components.
文摘An Intelligent Transportation System (ITS) is a new system developed for the betterment of user in traffic and transport management domain area for smart and safe driving. ITS subsystems are Emergency vehicle notification systems, Automatic road enforcement, Collision avoidance systems, Automatic parking, Map database management, etc. Advance Driver Assists System (ADAS) belongs to ITS which provides alert or warning or information to the user during driving. The proposed method uses Gaussian filtering and Median filtering to remove noise in the image. Subsequently image subtraction is achieved by subtracting Median filtered image from Gaussian filtered image. The resultant image is converted to binary image and the regions are analyzed using connected component approach. The prior work on speed bump detection is achieved using sensors which are failed to detect speed bumps that are constructed with small height and the detection rate is affected due to erroneous identification. And the smartphone and accelerometer methodologies are not perfectly suitable for real time scenario due to GPS error, network overload, real-time delay, accuracy and battery running out. The proposed system goes very well for the roads which are constructed with proper painting irrespective of their dimension.
文摘Let g and h be two transcendental entire functions. Suppose that the Fatou set F(goh) contains multiply connected components. In this article, we will consider the growth of the functions g and h.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11871404,11971398 and 12131018)。
文摘Let A be a basic connected finite dimensional associative algebra over an algebraically closed field k and G be a cyclic group.There is a quiver QGwith relationsρG such that the skew group algebras A[G]is Morita equivalent to the quotient algebra of path algebra kQGmodulo ideal(ρG).Generally,the quiver QGis not connected.In this paper we develop a method to determine the number of connect components of QG.Meanwhile,we introduce the notion of weight for underlying quiver of A such that A is G-graded and determine the connect components of smash product A#kG*.
基金supported by“Human Resources Program in Energy Technology”of the Korea Institute of Energy Technology Evaluation and Planning(KETEP),granted financial resources from theMinistry of Trade,Industry&Energy,Republic ofKorea(No.20204010600090).In addition,it was funded from the National Center of Artificial Intelligence(NCAI),Higher Education Commission,Pakistan,Grant/Award Number:Grant 2(1064).
文摘Brain tumor significantly impacts the quality of life and changes everything for a patient and their loved ones.Diagnosing a brain tumor usually begins with magnetic resonance imaging(MRI).The manual brain tumor diagnosis from the MRO images always requires an expert radiologist.However,this process is time-consuming and costly.Therefore,a computerized technique is required for brain tumor detection in MRI images.Using the MRI,a novel mechanism of the three-dimensional(3D)Kronecker convolution feature pyramid(KCFP)is used to segment brain tumors,resolving the pixel loss and weak processing of multi-scale lesions.A single dilation rate was replaced with the 3D Kronecker convolution,while local feature learning was performed using the 3D Feature Selection(3DFSC).A 3D KCFP was added at the end of 3DFSC to resolve weak processing of multi-scale lesions,yielding efficient segmentation of brain tumors of different sizes.A 3D connected component analysis with a global threshold was used as a post-processing technique.The standard Multimodal Brain Tumor Segmentation 2020 dataset was used for model validation.Our 3D KCFP model performed exceptionally well compared to other benchmark schemes with a dice similarity coefficient of 0.90,0.80,and 0.84 for the whole tumor,enhancing tumor,and tumor core,respectively.Overall,the proposed model was efficient in brain tumor segmentation,which may facilitate medical practitioners for an appropriate diagnosis for future treatment planning.
基金The NSF(10971024)of Chinathe Specialized Research Fund(200802860024)for the Doctoral Program of Higher Educationthe NSF(BK2010393)of Jiangsu Province
文摘The commuting graph of an arbitrary ring R, denoted by Г(R), is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity and the diameter of Г(ZnS3). We show that Г(ZnS3) is connected if and only if n is not a prime number. If Г(ZnS3) is connected then diam(Г(ZnS3)) = 3, while ifГ(ZnS3) is disconnected then every connected component of Г(ZnS3) must be a complete graph with same size, and we completely determine the vertice set of every connected component.
文摘Different methods for revising propositional knowledge base have been proposed recently by several researchers, but all methods are intractable in the general case. For practical application, this paper presents a revision method in special case, and gives a corresponding polynomial algorithm as well as its parallel version on CREW PRAM.
基金Supported by NSFC(11401353)TYAL of ShanxiNatural Science Foundation of Shanxi Province(2016011005)
文摘Given a digraph D =(V, A), the competition graph G of D, denoted by C(D), has the same set of vertices as D and an edge between vertices x and y if and only if N;(x)∩N;(y)≠Ф. In this paper, we investigate the competition graphs of round digraphs and give a necessary and sufficient condition for these graphs to be hamiltonian.
文摘Let B(R^n) be the set of all n x n real matrices, Sr the set of all matrices with rank r, 0 ≤ r ≤ n, and Sr^# the number of arcwise connected components of Sr. It is well-known that Sn =GL(R^n) is a Lie group and also a smooth hypersurface in B(R^n) with the dimension n × n.
文摘Let G be a finite group with order g and S be a subring of the algebraic number field which contains the integral extension over Z generated by a g-th primitive root co of unity, and R(G) be the character ring of G. The prime spectrum of the commutative ring S×Z R(G) iv denoted by Spec(S×Z R(G)) and set π={p|p is a rational prime number such that p^-1 S}. We prove that when G is a regroup, a π'-group, or a finite Abelian group, the number of the connetted components of Spec( S×Z R (G) ) coincides with the number of the π-regular classes in G,
文摘The identification of objects in binary images is a fundamental task in image analysis and pattern recognition tasks. The Euler number of a binary image is an important topological measure which is used as a feature in image analysis. In this paper, a very fast algorithm for the detection and localization of the objects and the computation of the Euler number of a binary image is proposed. The proposed algorithm operates in one scan of the image and is based on the Image Block Representation (IBR) scheme. The proposed algorithm is more efficient than conventional pixel based algorithms in terms of execution speed and representation of the extracted information.
基金supported in part by the National Natural Science Foundation of China(No.51807112)。
文摘Direct current(DC)bus voltage stability is essential for the stable and reliable operation of a DC system.If an oscillation source can be quickly and accurately localized,the oscillation can be adequately eliminated.We propose a method based on the power spectral density for identifying the voltage oscillation source.Specifically,a DC distribution network model combined with the component connection method is developed,and the network is separated into multiple power modules.Compared with a conventional method,the proposed method does not require determining the model parameters of the entire power grid,which is typically challenging.Furthermore,combined with a novel judgment index,the oscillation source can be identified more intuitively and clearly to enhance the applicability to real power grids.The performance of the proposed method has been evaluated using the MATLAB/Simulink software and PLECS RT Box experimental platform.The simulation and experimental results verify that the proposed method can accurately identify oscillation sources in a DC distribution network.
基金Supported by National Natural Science Foundation of China (Grant No. 10671122) the first author is supported by Youth Foundation of Shanghai (Grant No. sdl10017) and also partly supported by Natural Science Foundation of Shanghai (Grant No. 10ZR1412500) the second author is partly supported by STCSM (Grant No. 09XD1402500)
文摘A graph is called a proper refinement of a star graph if it is a refinement of a star graph, but it is neither a star graph nor a complete graph. For a refinement of a star graph G with center c, let G* be the subgraph of G induced on the vertex set V(G) / {c or end vertices adjacent to c}. In this paper, we study the isomorphic classification of some finite commutative local rings R by investigating their zero-divisor graphs G=Г(R), which is a proper refinement of a star graph with exactly one center c. We determine all finite commutative local rings R such that G* has at least two connected components. We prove that the diameter of the induced graph G* is two if Z(R)2 ≠{0}, Z(R)3 = {0} and Gc is connected. We determine the structure of R which has two distinct nonadjacent vertices a, fl C Z(R)*/{c} such that the ideal [N(a)N(β)]{0} is generated by only one element of Z(R)*/{c}. We also completely determine the correspondence between commutative rings and finite complete graphs Kn with some end vertices adjacent to a single vertex of Kn.
基金Research supported by the Science Foundation of Shandong Province.
文摘In this paper,a sequential algorithm computing the all vertex pair distance matrix D and the path matrix Pis given.On a PRAM EREW model with p,1≤p≤n^2,processors,a parallel version of the sequential algorithm is shown.This method can also be used to get a parallel algorithm to compute transitive closure arrayof an undirected graph.The time complexify of the parallel algorithm is O(n^3/p).If D,P andare known,it is shown that the problems to find all connected components, to compute the diameter of an undirected graph,to determine the center of a directed graph and to search for a directed cycle with the minimum(maximum)length in a directed graph can all be solved in O(n^2/p^+ logp)time.
文摘It is a common practice to simulate some historical or test systems to validate the efficiency of new methods or concepts. However, there are only a small number of existing power system test cases, and validation and evaluation results, obtained using such a limited number of test cases, may not be deemed sufficient or convincing. In order to provide more available test cases, a new random graph generation algorithm, named ‘‘dualstage constructed random graph’’ algorithm, is proposed to effectively model the power grid topology. The algorithm generates a spanning tree to guarantee the connectivity of random graphs and is capable of controlling the number of lines precisely. No matter how much the average degree is,whether sparse or not, random graphs can be quickly formed to satisfy the requirements. An approach is developed to generate random graphs with prescribed numbers of connected components, in order to simulate the power grid topology under fault conditions. Our experimental study on several realistic power grid topologies proves that the proposed algorithm can quickly generate a large number of random graphs with the topology characteristics of real-world power grid.
基金the National Natural Science Foundation of China(No.11531011).
文摘The k-component edgeconnectivity cλk(G)of anon-completegraph G is themini mum number of edges whose deletion results in a graph with at least k components In this paper,we extend some results by Guo et al.(Appl Math Comput 334:401-406,2018)by determining the component edge connectivity of the locally twisted cubes LTQn,i.e.,cλk+1(LTQn)=kn-exk/2for 1≤2[n/2],n≥7,where exk=∑si=0ti2ti+∑si=02·i·2ti,and k is a positive integer with decomposition k=∑si=02ti such that to="log2k"and ti="log2(k-∑i-1 r=02tr)"for i≥1.As a by-product,we characterize the corresponding optimal solutions.