论文标题
关于边缘对称和重量对称的最短重量约束路径的顺序优化数字和猜想
Sequential Optimization Numbers and Conjecture about Edge-Symmetry and Weight-Symmetry Shortest Weight-Constrained Path
论文作者
论文摘要
本文定义了多维顺序优化数字，并证明了第一类的未签名的Stirling数字是一维顺序优化数字。本文给出了复发公式和多维顺序优化数字的上限。我们证明，由O_K（N，M）表示的K维顺序优化数字几乎在{O_K（N，A）}中，其中A属于[1，Eklog（N-1）+（N-1）+（EPI）^2/6（2^K-1）+M_1]，N是k-dimential percential percential percential percential percential percential percential percential-imentiAnitional and imagentional and pertanitization and pertanitization和m__1。通过k维扩展，可以将第一类的斯特林数量的许多成就转化为k维顺序优化数字的属性，我们提供了一些示例。最短的重量约束路径是NP完整问题[1]。在边缘对称性和重量对称性的情况下，我们将优化设置的定义用于设计二维Bellman-Ford算法来解决它。根据以下事实：p_1（n，m> m）小于或等于e^（-m_1），其中m = eLog（n-1）+e+m_1，m_1，m_1是一个正整数，p_1（n，m）是1维顺序优化数量的概率，该纸张可以预料到解决方案的概率，并具有较短的权重效率，以使重量及时地构成重点，以实现较短的重量，以实现重视效果，以实现较短的重量，以实现较短的重量，以实现较短的重量构成量1呈指数，随着算法复杂性的恒定项增加。大量仿真实验的结果与此猜想一致。
This paper defines multidimensional sequential optimization numbers and prove that the unsigned Stirling numbers of first kind are 1-dimensional sequential optimization numbers. This paper gives a recurrence formula and an upper bound of multidimensional sequential optimization numbers. We proof that the k-dimensional sequential optimization numbers, denoted by O_k (n,m), are almost in {O_k (n,a)}, where a belong to[1,eklog(n-1)+(epi)^2/6(2^k-1)+M_1], n is the size of k-dimensional sequential optimization numbers and M_1 is large positive integer. Many achievements of the Stirling numbers of first kind can be transformed into the properties of k-dimensional sequential optimization numbers by k-dimensional extension and we give some examples. Shortest weight-constrained path is NP-complete problem [1]. In the case of edge symmetry and weight symmetry, we use the definition of the optimization set to design 2-dimensional Bellman-Ford algorithm to solve it. According to the fact that P_1 (n,m>M) less than or equal to e^(-M_1 ), where M=elog(n-1)+e+M_1, M_1 is a positive integer and P_1 (n,m) is the probability of 1-dimensional sequential optimization numbers, this paper conjecture that the probability of solving edge-symmetry and weight-symmetry shortest weight-constrained path problem in polynomial time approaches 1 exponentially with the increase of constant term in algorithm complexity. The results of a large number of simulation experiments agree with this conjecture.
