Mathematical Analysis of Optimal Decision-Making for Search Problems on Finite Graphs

我们考虑了有限图上各种搜索问题及其相关问题的最优搜索和最优管理的数学基础，并研究了网络安全管理的数学。我们证明了对埋伏博弈中渗透者拥有宽度的模型的分析回到了前人研究中渗透者没有宽度的模型的分析。得到了具有调查费用和移动费用的搜索问题的最优策略应满足的必要条件。

We considered the basics of the mathematics for elucidation of optimal search and optimal management about the various kinds of search problems and the allied issues on a finite graph and we studied the mathematics of the security management of the network. We showed that the analysis of the model whom an infiltrator owned the width in an ambush game returns to the analysis of the model in the precedent study in which an infiltrator did not have width. We got the necessary condition that an optimal strategy should have satisfied of the explorer of a search problem with investigation expense and the movement expense.