We consider the Robber Locating Game, where an invisible moving robber tries to evade the pursuit of one or more helicopter cops, who send distance probes from anywhere on the graph. In this paper, we attempt to propose two useful constructions for general problems in this game: a state variable that describes the available game information for the cops, and a Cop Strategy Graph construction that presents all possibilities of the game given a deterministic cop strategy. Then we will use them, along with algorithms and pseudo-code, to explain the relationship between two graph parameters, the localization number and the subdivision number. Researchers have shown that the later has a linear relationship with the former, while the other direction does not. We will revisit their proofs, consolidate the essential correspondence between the two numbers via our proposed constructions, and show an explicit result for the non-linear relationship.

翻译：我们考虑强盗定位游戏，其中不可见的移动强盗试图逃避一架或多架直升机警察的追捕，警察可向图中任意位置发送距离探测信号。本文尝试为该游戏的一般问题提出两种实用构造：一种用于描述警察可用游戏信息的状态变量，以及一种基于确定性警察策略呈现所有游戏可能性的警察策略图构造。随后，我们将利用这些构造结合算法与伪代码，解释两个图参数——定位数与剖分数——之间的关系。已有研究表明，剖分数与定位数呈线性关系，而反向关系则不成立。我们将重新审视已有证明，通过所提构造巩固两个参数间的本质对应关系，并给出非线性关系的显式结果。