In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tr...In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tree colorable are given. Moreover, a series of uniquely tree colorable graphs are constructed.展开更多
This paper proposes a generic high-performance and low-time-overhead software control flow checking solution, graph-tree-based control flow checking （GTCFC） for space-borne commercial-off-the-shelf （COTS） processo...This paper proposes a generic high-performance and low-time-overhead software control flow checking solution, graph-tree-based control flow checking （GTCFC） for space-borne commercial-off-the-shelf （COTS） processors. A graph tree data structure with a topology similar to common trees is introduced to transform the control flow graphs of target programs. This together with design of IDs and signatures of its vertices and edges allows for an easy check of legality of actual branching during target program execution. As a result, the algorithm not only is capable of detecting all single and multiple branching errors with low latency and time overheads along with a linear-complexity space overhead, but also remains generic among arbitrary instruction sets and independent of any specific hardware. Tests of the algorithm using a COTS-processor-based onboard computer （OBC） of in-service ZDPS-1A pico-satellite products show that GTCFC can detect over 90% of the randomly injected and all-pattern-covering branching errors for different types of target programs, with performance and overheads consistent with the theoretical analysis; and beats well-established preeminent control flow checking algorithms in these dimensions. Furthermore, it is validated that GTCGC not only can be accommodated in pico-satellites conveniently with still sufficient system margins left, but also has the ability to minimize the risk of control flow errors being undetected in their space missions. Therefore, due to its effectiveness, efficiency, and compatibility, the GTCFC solution is ready for applications on COTS processors on pico-satellites in their real space missions.展开更多
For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which ...For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which are distance two apart receive labels differing by at least k. The λ′j,k-number of G is the minimum m of an m-L（j, k）-edge-labeling admitted by G.In this article, we study the L（1, 2）-edge-labeling for paths, cycles, complete graphs, complete multipartite graphs, infinite ？-regular trees and wheels.展开更多
The metric dimension dim（G） of a graph G is the minimum number of vertices such that every vertex of G is uniquely determined by its vector of distances to the chosen vertices. The zero forcing number Z（G） of a gr...The metric dimension dim（G） of a graph G is the minimum number of vertices such that every vertex of G is uniquely determined by its vector of distances to the chosen vertices. The zero forcing number Z（G） of a graph G is the minimum eardinality of a set S of black vertices （whereas vertices in V（G）／S are colored white） such that V（G） is turned black after finitely many applications of ＂the color-change rule＂： a white vertex is converted black if it is the only white neighbor of a black vertex. We show that dim（T） ≤Z（T） for a tree T, and that dim（G）≤Z（G）＋I if G is a unicyclic graph; along the way, we characterize trees T attaining dim（T） = Z（T）. For a general graph G, we introduce the ＂cycle rank conjecture＂. We conclude with a proof of dim（T） - 2 ≤ dim（T ＋ e） ≤dim（T） ＋ 1 for e∈ E（T）.展开更多
Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential time.Recently,there has been growing interest in end-t...Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential time.Recently,there has been growing interest in end-to-end deep neural networks for solving routing problems.However,such methods typically produce sequences of vertices,which make it difficult to apply them to general combinatorial optimization problems where the solution set consists of edges,as in various spanning tree problems.In this paper,we propose NeuroPrim,a novel framework for solving various spanning tree problems by defining a Markov decision process for general combinatorial optimization problems on graphs.Our approach reduces the action and state space using Prim's algorithm and trains the resulting model using REINFORCE.We apply our framework to three difficult problems on the Euclidean space:the degree-constrained minimum spanning tree problem,the minimum routing cost spanning tree problem and the Steiner tree problem in graphs.Experimental results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 vertices.Additionally,we find that our model has strong generalization ability with no significant degradation observed on problem instances as large as 1,000.Our results suggest that our framework can be effective for solving a wide range of combinatorial optimization problems beyond spanning tree problems.展开更多
The precise and effective measure results of Web applications not only facilitate good comprehension of them, but also benefit to the macro-management of software activities, such as testing, reverse engineering, reus...The precise and effective measure results of Web applications not only facilitate good comprehension of them, but also benefit to the macro-management of software activities, such as testing, reverse engineering, reuse, etc. The paper exploits some researches on measuring the structure complexity of Web application. Through a deep analysis of the configuration and objects＇ interactions of Web system, two conclusions have been drawn：① A generic Web application consists of static web page, dynamic page, component and database object; ② The main interactions have only three styles, that is static link, dynamic link and call/return relation. Based on analysis and modeling of the content of a Web page （static or dynamic）, complexity measure methods of both control logic of script and nesting of HTML code are further discussed. In addition, two methods for measuring the complexity of inte〉page navigation are also addressed by modeling the inte〉page navigation behaviors of Web application via WNG graph.展开更多
Network reconfiguration is of theoretical and practical significance to guarantee safe and economical operation of distribution system.In this paper,based on all spanning trees of undirected graph,a novel genetic algo...Network reconfiguration is of theoretical and practical significance to guarantee safe and economical operation of distribution system.In this paper,based on all spanning trees of undirected graph,a novel genetic algorithm for electric distribution network reconfiguration is proposed.Above all,all spanning trees of simplified graph of distribution network are found.Tie branches are obtained with spanning tree subtracted from simplified graph.There is one and only one switch open on each tie branch.Decimal identity number of open switch on each tie branch is taken as the optimization variable.Therefore,the length of chromosome is very short.Each spanning tree corresponds to one subpopulation.Gene operations of each subpopulation are implemented with parallel computing method.Individuals of offspring after gene operation automatically meet with radial and connected constraints for distribution network operation.Disadvantages of conventional genetic algorithm for network reconfiguration that a large amount of unfeasible solutions are created after crossover and mutation,which result in very low searching efficiency,are completely overcome.High calculation speed and superior capability of the proposed method are validated by two test cases.展开更多
The spectrum of a graph is the set of all eigenvalues of the Laplacian matrix of the graph. There is a closed relationship between the Laplacian spectrum of graphs and some properties of graphs such as connectivity. I...The spectrum of a graph is the set of all eigenvalues of the Laplacian matrix of the graph. There is a closed relationship between the Laplacian spectrum of graphs and some properties of graphs such as connectivity. In the recent years Laplacian spectrum of graphs has been widely applied in many fields. The application of Laplacian spectrum of graphs to circuit partitioning problems is reviewed in this paper. A new criterion of circuit partitioning is proposed and the bounds of the partition ratio for weighted graphs are also presented. Moreover, the deficiency of graph-partitioning algorithms by Laplacian eigenvectors is addressed and an algorithm by means of the minimal spanning tree of a graph is proposed. By virtue of taking the graph structure into consideration this algorithm can fulfill general requirements of circuit partitioning.展开更多
The condition of the road infrastructure has severe impacts on the road safety, driving comfort, and on the rolling resistance. Therefore, the road infrastructure must be moni- tored comprehensively and in regular int...The condition of the road infrastructure has severe impacts on the road safety, driving comfort, and on the rolling resistance. Therefore, the road infrastructure must be moni- tored comprehensively and in regular intervals to identify damaged road segments and road hazards. Methods have been developed to comprehensively and automatically digitize the road infrastructure and estimate the road quality, which are based on vehicle sensors and a supervised machine learning classification. Since different types of vehicles have various suspension systems with different response functions, one classifier cannot be taken over to other vehicles. Usually, a high amount of time is needed to acquire training data for each individual vehicle and classifier. To address this problem, the methods to collect training data automatically for new vehicles based on the comparison of trajectories of untrained and trained vehicles have been developed. The results show that the method based on a k-dimensional tree and Euclidean distance performs best and is robust in transferring the information of the road surface from one vehicle to another. Furthermore, this method offers the possibility to merge the output and road infrastructure information from multiple vehicles to enable a more robust and precise prediction of the ground truth.展开更多
In this paper, we deal with the problem of selecting the location of coal concentratedstation. Where should we found the station, in a certain range, to mininize the total transporting cost ? The corresponding mathema...In this paper, we deal with the problem of selecting the location of coal concentratedstation. Where should we found the station, in a certain range, to mininize the total transporting cost ? The corresponding mathematical model will be founded. Furthermore, we prove that S reaches its minimum at its certain vertex. An algorithm used to find the optimum solution will be given.展开更多
文摘In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tree colorable are given. Moreover, a series of uniquely tree colorable graphs are constructed.
基金supported by National Natural Science Foundation of China (No. 60904090)
文摘This paper proposes a generic high-performance and low-time-overhead software control flow checking solution, graph-tree-based control flow checking （GTCFC） for space-borne commercial-off-the-shelf （COTS） processors. A graph tree data structure with a topology similar to common trees is introduced to transform the control flow graphs of target programs. This together with design of IDs and signatures of its vertices and edges allows for an easy check of legality of actual branching during target program execution. As a result, the algorithm not only is capable of detecting all single and multiple branching errors with low latency and time overheads along with a linear-complexity space overhead, but also remains generic among arbitrary instruction sets and independent of any specific hardware. Tests of the algorithm using a COTS-processor-based onboard computer （OBC） of in-service ZDPS-1A pico-satellite products show that GTCFC can detect over 90% of the randomly injected and all-pattern-covering branching errors for different types of target programs, with performance and overheads consistent with the theoretical analysis; and beats well-established preeminent control flow checking algorithms in these dimensions. Furthermore, it is validated that GTCGC not only can be accommodated in pico-satellites conveniently with still sufficient system margins left, but also has the ability to minimize the risk of control flow errors being undetected in their space missions. Therefore, due to its effectiveness, efficiency, and compatibility, the GTCFC solution is ready for applications on COTS processors on pico-satellites in their real space missions.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1097102510901035)
文摘For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which are distance two apart receive labels differing by at least k. The λ′j,k-number of G is the minimum m of an m-L（j, k）-edge-labeling admitted by G.In this article, we study the L（1, 2）-edge-labeling for paths, cycles, complete graphs, complete multipartite graphs, infinite ？-regular trees and wheels.
文摘The metric dimension dim（G） of a graph G is the minimum number of vertices such that every vertex of G is uniquely determined by its vector of distances to the chosen vertices. The zero forcing number Z（G） of a graph G is the minimum eardinality of a set S of black vertices （whereas vertices in V（G）／S are colored white） such that V（G） is turned black after finitely many applications of ＂the color-change rule＂： a white vertex is converted black if it is the only white neighbor of a black vertex. We show that dim（T） ≤Z（T） for a tree T, and that dim（G）≤Z（G）＋I if G is a unicyclic graph; along the way, we characterize trees T attaining dim（T） = Z（T）. For a general graph G, we introduce the ＂cycle rank conjecture＂. We conclude with a proof of dim（T） - 2 ≤ dim（T ＋ e） ≤dim（T） ＋ 1 for e∈ E（T）.
基金supported by National Key R&D Program of China(Grant No.2021YFA1000403)National Natural Science Foundation of China(Grant No.11991022)+1 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA27000000)the Fundamental Research Funds for the Central Universities。
文摘Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential time.Recently,there has been growing interest in end-to-end deep neural networks for solving routing problems.However,such methods typically produce sequences of vertices,which make it difficult to apply them to general combinatorial optimization problems where the solution set consists of edges,as in various spanning tree problems.In this paper,we propose NeuroPrim,a novel framework for solving various spanning tree problems by defining a Markov decision process for general combinatorial optimization problems on graphs.Our approach reduces the action and state space using Prim's algorithm and trains the resulting model using REINFORCE.We apply our framework to three difficult problems on the Euclidean space:the degree-constrained minimum spanning tree problem,the minimum routing cost spanning tree problem and the Steiner tree problem in graphs.Experimental results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 vertices.Additionally,we find that our model has strong generalization ability with no significant degradation observed on problem instances as large as 1,000.Our results suggest that our framework can be effective for solving a wide range of combinatorial optimization problems beyond spanning tree problems.
基金Supported by the Defense Pre-Research Project ofthe 10th Five-Year Plan of China (413150902) ,andthe Defense Pre-Research Project of the Navy Equipment Ministry (10104010201)
文摘The precise and effective measure results of Web applications not only facilitate good comprehension of them, but also benefit to the macro-management of software activities, such as testing, reverse engineering, reuse, etc. The paper exploits some researches on measuring the structure complexity of Web application. Through a deep analysis of the configuration and objects＇ interactions of Web system, two conclusions have been drawn：① A generic Web application consists of static web page, dynamic page, component and database object; ② The main interactions have only three styles, that is static link, dynamic link and call/return relation. Based on analysis and modeling of the content of a Web page （static or dynamic）, complexity measure methods of both control logic of script and nesting of HTML code are further discussed. In addition, two methods for measuring the complexity of inte〉page navigation are also addressed by modeling the inte〉page navigation behaviors of Web application via WNG graph.
文摘Network reconfiguration is of theoretical and practical significance to guarantee safe and economical operation of distribution system.In this paper,based on all spanning trees of undirected graph,a novel genetic algorithm for electric distribution network reconfiguration is proposed.Above all,all spanning trees of simplified graph of distribution network are found.Tie branches are obtained with spanning tree subtracted from simplified graph.There is one and only one switch open on each tie branch.Decimal identity number of open switch on each tie branch is taken as the optimization variable.Therefore,the length of chromosome is very short.Each spanning tree corresponds to one subpopulation.Gene operations of each subpopulation are implemented with parallel computing method.Individuals of offspring after gene operation automatically meet with radial and connected constraints for distribution network operation.Disadvantages of conventional genetic algorithm for network reconfiguration that a large amount of unfeasible solutions are created after crossover and mutation,which result in very low searching efficiency,are completely overcome.High calculation speed and superior capability of the proposed method are validated by two test cases.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.60025101 and 90207001)by the National Basic Research Priorities Program(Contract No.G1999032903).
文摘The spectrum of a graph is the set of all eigenvalues of the Laplacian matrix of the graph. There is a closed relationship between the Laplacian spectrum of graphs and some properties of graphs such as connectivity. In the recent years Laplacian spectrum of graphs has been widely applied in many fields. The application of Laplacian spectrum of graphs to circuit partitioning problems is reviewed in this paper. A new criterion of circuit partitioning is proposed and the bounds of the partition ratio for weighted graphs are also presented. Moreover, the deficiency of graph-partitioning algorithms by Laplacian eigenvectors is addressed and an algorithm by means of the minimal spanning tree of a graph is proposed. By virtue of taking the graph structure into consideration this algorithm can fulfill general requirements of circuit partitioning.
基金project of Technical Aspects of Monitoring the Acoustic Quality of Infrastructure in Road Transport(3714541000)commissioned by the German Federal Environment Agencyfunded by the Federal Ministry for the Environment,Nature Conservation,Building and Nuclear Safety,Germany,within the Environmental Research Plan 2014.
文摘The condition of the road infrastructure has severe impacts on the road safety, driving comfort, and on the rolling resistance. Therefore, the road infrastructure must be moni- tored comprehensively and in regular intervals to identify damaged road segments and road hazards. Methods have been developed to comprehensively and automatically digitize the road infrastructure and estimate the road quality, which are based on vehicle sensors and a supervised machine learning classification. Since different types of vehicles have various suspension systems with different response functions, one classifier cannot be taken over to other vehicles. Usually, a high amount of time is needed to acquire training data for each individual vehicle and classifier. To address this problem, the methods to collect training data automatically for new vehicles based on the comparison of trajectories of untrained and trained vehicles have been developed. The results show that the method based on a k-dimensional tree and Euclidean distance performs best and is robust in transferring the information of the road surface from one vehicle to another. Furthermore, this method offers the possibility to merge the output and road infrastructure information from multiple vehicles to enable a more robust and precise prediction of the ground truth.
文摘In this paper, we deal with the problem of selecting the location of coal concentratedstation. Where should we found the station, in a certain range, to mininize the total transporting cost ? The corresponding mathematical model will be founded. Furthermore, we prove that S reaches its minimum at its certain vertex. An algorithm used to find the optimum solution will be given.
