Random Sampling of Euler Tours

We define a Markov chain on the set of Euler tours of a given Eulerian graph based on transformations first defined by Kotzig in 1966. We prove that the chain is rapidly mixing if the maximum degree in the given graph is 6, thus obtaining an efficient algorithm for sampling and counting the set of Euler tours for such an Eulerian graph. Received October 30, 1997; revised March 12, 1999, and April 17, 2000.     

随机数发生器对蒙特卡罗算法求解定积分的影响

在运用蒙特卡罗算法求解定积分的解时 ,程序中的核心问题是随机数发生器的选用 ,选用不同的随机数发生器对定积分的计算结果有着不同的计算精度。通过选用三种不同的随机数发生器 ,对蒙特卡罗算法求解定积分进行此较实验 ,选出一个计算精度较高的随机数发生器 ,并对其所需参数进行对比选择。