Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem （GIP） is a nondeterministic polynomial problem. A simulated annea...Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem （GIP） is a nondeterministic polynomial problem. A simulated annealing （SA） algorithm for detecting graph isomorphism is proposed, and the proposed SA algorithm is well suited to deal with random graphs with large size. To verify the validity of the proposed SA algorithm, simulations are performed on three pairs of small graphs and four pairs of large random graphs with edge densities 0.5, 0.1, and 0.01, respectively. The simulation results show that the proposed SA algorithm can detect graph isomorphism with a high probability.展开更多
对于无向连通图G(V,E),若存在一个单映射f:V(G)∪E(G)→{1,2,…,|V|+|E|},如果uv∈E(G)且d(u)=d(v),有S(u)=S(v),其中S(u)=f(u)+∑/uz∈E(G)f(uz),d(u)表示点u的度,则称f为G的邻点可约全标号(adjacent vertex reducible total labeling,...对于无向连通图G(V,E),若存在一个单映射f:V(G)∪E(G)→{1,2,…,|V|+|E|},如果uv∈E(G)且d(u)=d(v),有S(u)=S(v),其中S(u)=f(u)+∑/uz∈E(G)f(uz),d(u)表示点u的度,则称f为G的邻点可约全标号(adjacent vertex reducible total labeling,AVRTL)。结合遗传算法和粒子群算法设计一种启发式搜索算法,可以判断有限点内随机图是否存在AVRTL。通过对实验结果分析,总结了若干联图的定理并给出证明。得到结论:如果子图G_(1)和G_(2)是AVRTL图,则图运算↑ab具有封闭性,即联图G_(1)↑_(ab)G_(2)亦为AVRTL图。展开更多
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
为了提高异构多核处理器平台的计算性能,从任务调度的角度出发,提出了一种使用黄金正弦和莱维飞行机制改进的麻雀搜索算法(Fusion of Golden Sinusoidal and Levy Flight in Sparrow Search Algorithm,GSLF-SSA)来优化异构多核处理器的...为了提高异构多核处理器平台的计算性能,从任务调度的角度出发,提出了一种使用黄金正弦和莱维飞行机制改进的麻雀搜索算法(Fusion of Golden Sinusoidal and Levy Flight in Sparrow Search Algorithm,GSLF-SSA)来优化异构多核处理器的任务调度。通过对异构任务调度的分析,将异构任务建模为DAG(Directed Acyclic Graph)任务模型,通过对其优先级进行随机编码分配,实现了GSLF-SSA算法求解域从连续到离散的映射,使该算法更能适用于异构多核任务调度之中。将DAG任务的最优调度长度作为算法的适应度值进行迭代寻优,通过与目前应用广泛的麻雀搜索算法(SSA)、混合式任务调度算法(IHSSA)、人工蜂群算法(ABC)等多种启发式算法在异构任务调度环境下的实验对比表明,GSLF-SSA能获得更优的调度长度与更短的调度执行时间。展开更多
基金the National Natural Science Foundation of China (60373089, 60674106, and 60533010)the National High Technology Research and Development "863" Program (2006AA01Z104)
文摘Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem （GIP） is a nondeterministic polynomial problem. A simulated annealing （SA） algorithm for detecting graph isomorphism is proposed, and the proposed SA algorithm is well suited to deal with random graphs with large size. To verify the validity of the proposed SA algorithm, simulations are performed on three pairs of small graphs and four pairs of large random graphs with edge densities 0.5, 0.1, and 0.01, respectively. The simulation results show that the proposed SA algorithm can detect graph isomorphism with a high probability.
文摘对于无向连通图G(V,E),若存在一个单映射f:V(G)∪E(G)→{1,2,…,|V|+|E|},如果uv∈E(G)且d(u)=d(v),有S(u)=S(v),其中S(u)=f(u)+∑/uz∈E(G)f(uz),d(u)表示点u的度,则称f为G的邻点可约全标号(adjacent vertex reducible total labeling,AVRTL)。结合遗传算法和粒子群算法设计一种启发式搜索算法,可以判断有限点内随机图是否存在AVRTL。通过对实验结果分析,总结了若干联图的定理并给出证明。得到结论:如果子图G_(1)和G_(2)是AVRTL图,则图运算↑ab具有封闭性,即联图G_(1)↑_(ab)G_(2)亦为AVRTL图。
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).
文摘为了提高异构多核处理器平台的计算性能,从任务调度的角度出发,提出了一种使用黄金正弦和莱维飞行机制改进的麻雀搜索算法(Fusion of Golden Sinusoidal and Levy Flight in Sparrow Search Algorithm,GSLF-SSA)来优化异构多核处理器的任务调度。通过对异构任务调度的分析,将异构任务建模为DAG(Directed Acyclic Graph)任务模型,通过对其优先级进行随机编码分配,实现了GSLF-SSA算法求解域从连续到离散的映射,使该算法更能适用于异构多核任务调度之中。将DAG任务的最优调度长度作为算法的适应度值进行迭代寻优,通过与目前应用广泛的麻雀搜索算法(SSA)、混合式任务调度算法(IHSSA)、人工蜂群算法(ABC)等多种启发式算法在异构任务调度环境下的实验对比表明,GSLF-SSA能获得更优的调度长度与更短的调度执行时间。
