Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-hard combinatoria...Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-hard combinatorial optimization problem,which is widely applied in communication networks,multimodal transportation networks,and data compression.Some approximation algorithms and heuristics algorithms have been proposed for the problem.Firefly algorithm is a new meta-heuristic algorithm.Because of its simplicity and easy implementation,it has been successfully applied in various fields.However,the basic firefly algorithm is not suitable for discrete problems.To this end,a novel discrete firefly algorithm for the MLST problem is proposed in this paper.A binary operation method to update firefly positions and a local feasible handling method are introduced,which correct unfeasible solutions,eliminate redundant labels,and make the algorithm more suitable for discrete problems.Computational results show that the algorithm has good performance.The algorithm can be extended to solve other discrete optimization problems.展开更多
It is proposed a high resolution remote sensing image segmentation method which combines static minimum spanning tree(MST)tessellation considering shape information and the RHMRF-FCM algorithm.It solves the problems i...It is proposed a high resolution remote sensing image segmentation method which combines static minimum spanning tree(MST)tessellation considering shape information and the RHMRF-FCM algorithm.It solves the problems in the traditional pixel-based HMRF-FCM algorithm in which poor noise resistance and low precision segmentation in a complex boundary exist.By using the MST model and shape information,the object boundary and geometrical noise can be expressed and reduced respectively.Firstly,the static MST tessellation is employed for dividing the image domain into some sub-regions corresponding to the components of homogeneous regions needed to be segmented.Secondly,based on the tessellation results,the RHMRF model is built,and regulation terms considering the KL information and the information entropy are introduced into the FCM objective function.Finally,the partial differential method and Lagrange function are employed to calculate the parameters of the fuzzy objective function for obtaining the global optimal segmentation results.To verify the robustness and effectiveness of the proposed algorithm,the experiments are carried out with WorldView-3(WV-3)high resolution image.The results from proposed method with different parameters and comparing methods(multi-resolution method and watershed segmentation method in eCognition software)are analyzed qualitatively and quantitatively.展开更多
This paper provides a method of producing a minimum cost spanning tree(MCST)using set operations.It studies the data structure for implementation of set operations and the algorithm to be applied to this structure and...This paper provides a method of producing a minimum cost spanning tree(MCST)using set operations.It studies the data structure for implementation of set operations and the algorithm to be applied to this structure and proves the correctness and the complexity of the algorithm.This algorithm uses the FDG(formula to divide elements into groups)to sort(the FDG sorts a sequence of n elements in expected tir O(n))and uses the method of path compression to find and to unite.Therefore.n produces an MCST of an undirected network having n vertices and e edges in expected time O(eG(n)).展开更多
Based on the graphic theory and improved genetic algorithm,an improved genetic algorithm to search the minimum spanning trees is given . The algorithm uses binary code to represent the problem of minimum spanning tree...Based on the graphic theory and improved genetic algorithm,an improved genetic algorithm to search the minimum spanning trees is given . The algorithm uses binary code to represent the problem of minimum spanning trees. It designs the corresponding fitness function,operator and few controlling strategies to improve its speed and evolutionary efficiency.Only one solution can be gotten with running traditional al-gorithem atone time.The new algorithm can get a set of the solutions with higher probability in a shorter time.The experiment shows that it has a better performance than traditional methods.展开更多
Molecular programming is applied to minimum spanning problem whose solution requires encoding of real values in DNA strands. A new encoding scheme is proposed for real values that is biologically plausible and has a f...Molecular programming is applied to minimum spanning problem whose solution requires encoding of real values in DNA strands. A new encoding scheme is proposed for real values that is biologically plausible and has a fixed code length. According to the characteristics of the problem, a DNA algorithm solving the minimum spanning tree problem is given. The effectiveness of the proposed method is verified by simulation. The advantages and disadvantages of this algorithm are discussed.展开更多
Unmanned aerial vehicles(UAVs) enable flexible networking functions in emergency scenarios.However,due to the movement characteristic of ground users(GUs),it is challenging to capture the interactions among GUs.Thus,w...Unmanned aerial vehicles(UAVs) enable flexible networking functions in emergency scenarios.However,due to the movement characteristic of ground users(GUs),it is challenging to capture the interactions among GUs.Thus,we propose a learningbased dynamic connectivity maintenance architecture to reduce the delay for the UAV-assisted device-todevice(D2D) multicast communication.In this paper,each UAV transmits information to a selected GU,and then other GUs receive the information in a multi-hop manner.To minimize the total delay while ensuring that all GUs receive the information,we decouple it into three subproblems according to the time division on the topology:For the cluster-head selection,we adopt the Whale Optimization Algorithm(WOA) to imitate the hunting behavior of whales by abstracting the UAVs and cluster-heads into whales and preys,respectively;For the D2D multi-hop link establishment,we make the best of social relationships between GUs,and propose a node mapping algorithm based on the balanced spanning tree(BST) with reconfiguration to minimize the number of hops;For the dynamic connectivity maintenance,Restricted Q-learning(RQL) is utilized to learn the optimal multicast timeslot.Finally,the simulation results show that our proposed algorithms perfor better than other benchmark algorithms in the dynamic scenario.展开更多
The reconfigurable mesh consists of an array of processors interconnected by a reconfigurable bus system. The bus system can be used to dynamically obtain various interconnection patterns among the processors. Recent...The reconfigurable mesh consists of an array of processors interconnected by a reconfigurable bus system. The bus system can be used to dynamically obtain various interconnection patterns among the processors. Recently, this model has attracted a lot of attention. In this paper, two efficient algorithms are proposed for computing the minimum spanning tree of an n-vertex undirected graph. One runs on an n×n reconfigurable mesh with time complexity of O(log^2 n). The other runs with time complexity of O(log n) on an n^(1+E)×n reconfigurable mesh, where < E < 1 is a constant. All these improve the previously known results on the reconfigurable mesh.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
We address the 1-line minimum Steiner tree of line segments(1L-MStT-LS)problem.Specifically,given a set S of n disjoint line segments in R^(2),we are asked to find the location of a line l and a set E_(l) of necessary...We address the 1-line minimum Steiner tree of line segments(1L-MStT-LS)problem.Specifically,given a set S of n disjoint line segments in R^(2),we are asked to find the location of a line l and a set E_(l) of necessary line segments(i.e.,edges)such that a graph consisting of all line segments in S ∪ E_(l) plus this line l,denoted by T_(l)=(S,l,E_(l)),becomes a Steiner tree,the objective is to minimize total length of edges in E_(l) among all such Steiner trees.Similarly,we are asked to find a set E_(0) of necessary edges such that a graph consisting of all line segments in S ∪ E_(0),denoted by T_(S)=(S,E_(0)),becomes a Steiner tree,the objective is to minimize total length of edges in E_(0) among all such Steiner trees,we refer to this new problem as the minimum Steiner tree of line segments(MStT-LS)problem.In addition,when two endpoints of each edge in Eo need to be located on two different line segments in S,respectively,we refer to that problem as the minimum spanning tree of line segments(MST-LS)problem.We obtain three main results:(1)Using technique of Voronoi diagram of line segments,we design an exact algorithm in time O(n log n)to solve the MST-LS problem;(2)we show that the algorithm designed in(1)is a 1.214-approximation algorithm to solve the MStT-LS problem;(3)using the combination of the algorithm designed in(1)as a subroutine for many times,a technique of finding linear facility location and a key lemma proved by techniques of computational geometry,we present a 1.214-approximation algorithm in time O(n^(3) log n)to solve the 1L-MStT-LS problem.展开更多
It’s a very popular issue regarding the minimum cost spanning tree which is of great practical and economical significance to solve it in a concise and accelerated way. In this paper, the basic ideas of Kruskal algor...It’s a very popular issue regarding the minimum cost spanning tree which is of great practical and economical significance to solve it in a concise and accelerated way. In this paper, the basic ideas of Kruskal algorithm were discussed and then presented a new improved algorithm—two branch Kruskal algorithm, which is improved to choose a middle value. Finally, because the time complexity is reduced, and the process is more convenient, it is concluded that the improved Kruskal algorithm is more effective in most cases compared with the Kruskal algorithm.展开更多
The extension of Minimum Spanning Tree(MST) problem is an NP hard problem which does not exit a polynomial time algorithm. In this paper, a fast optimization method on MST problem——the Gradient Gene Algorithm is int...The extension of Minimum Spanning Tree(MST) problem is an NP hard problem which does not exit a polynomial time algorithm. In this paper, a fast optimization method on MST problem——the Gradient Gene Algorithm is introduced. Compared with other evolutionary algorithms on MST problem, it is more advanced: firstly, very simple and easy to realize; then, efficient and accurate; finally general on other combination optimization problems.展开更多
基金This work is supported by the National Natural Science Foundation of China under Grant 61772179the Hunan Provincial Natural Science Foundation of China under Grant 2019JJ40005+3 种基金the Science and Technology Plan Project of Hunan Province under Grant 2016TP1020the Double First-Class University Project of Hunan Province under Grant Xiangjiaotong[2018]469the Open Fund Project of Hunan Provincial Key Laboratory of Intelligent Information Processing and Application for Hengyang Normal University under Grant IIPA19K02the Science Foundation of Hengyang Normal University under Grant 19QD13.
文摘Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-hard combinatorial optimization problem,which is widely applied in communication networks,multimodal transportation networks,and data compression.Some approximation algorithms and heuristics algorithms have been proposed for the problem.Firefly algorithm is a new meta-heuristic algorithm.Because of its simplicity and easy implementation,it has been successfully applied in various fields.However,the basic firefly algorithm is not suitable for discrete problems.To this end,a novel discrete firefly algorithm for the MLST problem is proposed in this paper.A binary operation method to update firefly positions and a local feasible handling method are introduced,which correct unfeasible solutions,eliminate redundant labels,and make the algorithm more suitable for discrete problems.Computational results show that the algorithm has good performance.The algorithm can be extended to solve other discrete optimization problems.
基金National Natural Science Foundation of China(No.41271435)National Natural Science Foundation of China Youth Found(No.41301479)。
文摘It is proposed a high resolution remote sensing image segmentation method which combines static minimum spanning tree(MST)tessellation considering shape information and the RHMRF-FCM algorithm.It solves the problems in the traditional pixel-based HMRF-FCM algorithm in which poor noise resistance and low precision segmentation in a complex boundary exist.By using the MST model and shape information,the object boundary and geometrical noise can be expressed and reduced respectively.Firstly,the static MST tessellation is employed for dividing the image domain into some sub-regions corresponding to the components of homogeneous regions needed to be segmented.Secondly,based on the tessellation results,the RHMRF model is built,and regulation terms considering the KL information and the information entropy are introduced into the FCM objective function.Finally,the partial differential method and Lagrange function are employed to calculate the parameters of the fuzzy objective function for obtaining the global optimal segmentation results.To verify the robustness and effectiveness of the proposed algorithm,the experiments are carried out with WorldView-3(WV-3)high resolution image.The results from proposed method with different parameters and comparing methods(multi-resolution method and watershed segmentation method in eCognition software)are analyzed qualitatively and quantitatively.
文摘This paper provides a method of producing a minimum cost spanning tree(MCST)using set operations.It studies the data structure for implementation of set operations and the algorithm to be applied to this structure and proves the correctness and the complexity of the algorithm.This algorithm uses the FDG(formula to divide elements into groups)to sort(the FDG sorts a sequence of n elements in expected tir O(n))and uses the method of path compression to find and to unite.Therefore.n produces an MCST of an undirected network having n vertices and e edges in expected time O(eG(n)).
文摘Based on the graphic theory and improved genetic algorithm,an improved genetic algorithm to search the minimum spanning trees is given . The algorithm uses binary code to represent the problem of minimum spanning trees. It designs the corresponding fitness function,operator and few controlling strategies to improve its speed and evolutionary efficiency.Only one solution can be gotten with running traditional al-gorithem atone time.The new algorithm can get a set of the solutions with higher probability in a shorter time.The experiment shows that it has a better performance than traditional methods.
文摘Molecular programming is applied to minimum spanning problem whose solution requires encoding of real values in DNA strands. A new encoding scheme is proposed for real values that is biologically plausible and has a fixed code length. According to the characteristics of the problem, a DNA algorithm solving the minimum spanning tree problem is given. The effectiveness of the proposed method is verified by simulation. The advantages and disadvantages of this algorithm are discussed.
基金supported by the Future Scientists Program of China University of Mining and Technology(2020WLKXJ030)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX201993).
文摘Unmanned aerial vehicles(UAVs) enable flexible networking functions in emergency scenarios.However,due to the movement characteristic of ground users(GUs),it is challenging to capture the interactions among GUs.Thus,we propose a learningbased dynamic connectivity maintenance architecture to reduce the delay for the UAV-assisted device-todevice(D2D) multicast communication.In this paper,each UAV transmits information to a selected GU,and then other GUs receive the information in a multi-hop manner.To minimize the total delay while ensuring that all GUs receive the information,we decouple it into three subproblems according to the time division on the topology:For the cluster-head selection,we adopt the Whale Optimization Algorithm(WOA) to imitate the hunting behavior of whales by abstracting the UAVs and cluster-heads into whales and preys,respectively;For the D2D multi-hop link establishment,we make the best of social relationships between GUs,and propose a node mapping algorithm based on the balanced spanning tree(BST) with reconfiguration to minimize the number of hops;For the dynamic connectivity maintenance,Restricted Q-learning(RQL) is utilized to learn the optimal multicast timeslot.Finally,the simulation results show that our proposed algorithms perfor better than other benchmark algorithms in the dynamic scenario.
基金Ph.D.foundation of Sate Education Commission of China
文摘The reconfigurable mesh consists of an array of processors interconnected by a reconfigurable bus system. The bus system can be used to dynamically obtain various interconnection patterns among the processors. Recently, this model has attracted a lot of attention. In this paper, two efficient algorithms are proposed for computing the minimum spanning tree of an n-vertex undirected graph. One runs on an n×n reconfigurable mesh with time complexity of O(log^2 n). The other runs with time complexity of O(log n) on an n^(1+E)×n reconfigurable mesh, where < E < 1 is a constant. All these improve the previously known results on the reconfigurable mesh.
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 National Natural Science Foundation of China(Nos.11861075 and 12101593)Project for Innovation Team(Cultivation)of Yunnan Province(No.202005AE160006)+2 种基金Key Project of Yunnan Provincial Science and Technology Department and Yunnan University(No.2018FY001014)Program for Innovative Research Team(in Science and Technology)in Universities of Yunnan Province(No.C176240111009)Jian-Ping Li is also supported by Project of Yunling Scholars Training of Yunnan Province.Su-Ding Liu is also supported by the Graduate Research and Innovation Project of Yunnan University(No.2020Z66).
文摘We address the 1-line minimum Steiner tree of line segments(1L-MStT-LS)problem.Specifically,given a set S of n disjoint line segments in R^(2),we are asked to find the location of a line l and a set E_(l) of necessary line segments(i.e.,edges)such that a graph consisting of all line segments in S ∪ E_(l) plus this line l,denoted by T_(l)=(S,l,E_(l)),becomes a Steiner tree,the objective is to minimize total length of edges in E_(l) among all such Steiner trees.Similarly,we are asked to find a set E_(0) of necessary edges such that a graph consisting of all line segments in S ∪ E_(0),denoted by T_(S)=(S,E_(0)),becomes a Steiner tree,the objective is to minimize total length of edges in E_(0) among all such Steiner trees,we refer to this new problem as the minimum Steiner tree of line segments(MStT-LS)problem.In addition,when two endpoints of each edge in Eo need to be located on two different line segments in S,respectively,we refer to that problem as the minimum spanning tree of line segments(MST-LS)problem.We obtain three main results:(1)Using technique of Voronoi diagram of line segments,we design an exact algorithm in time O(n log n)to solve the MST-LS problem;(2)we show that the algorithm designed in(1)is a 1.214-approximation algorithm to solve the MStT-LS problem;(3)using the combination of the algorithm designed in(1)as a subroutine for many times,a technique of finding linear facility location and a key lemma proved by techniques of computational geometry,we present a 1.214-approximation algorithm in time O(n^(3) log n)to solve the 1L-MStT-LS problem.
文摘It’s a very popular issue regarding the minimum cost spanning tree which is of great practical and economical significance to solve it in a concise and accelerated way. In this paper, the basic ideas of Kruskal algorithm were discussed and then presented a new improved algorithm—two branch Kruskal algorithm, which is improved to choose a middle value. Finally, because the time complexity is reduced, and the process is more convenient, it is concluded that the improved Kruskal algorithm is more effective in most cases compared with the Kruskal algorithm.
文摘The extension of Minimum Spanning Tree(MST) problem is an NP hard problem which does not exit a polynomial time algorithm. In this paper, a fast optimization method on MST problem——the Gradient Gene Algorithm is introduced. Compared with other evolutionary algorithms on MST problem, it is more advanced: firstly, very simple and easy to realize; then, efficient and accurate; finally general on other combination optimization problems.
