Competitive search in a network
Competitive search in a network
复制标题
网络中的竞争性搜索
DOI：
10.1016/j.ejor.2020.04.003
复制
发表时间：
2020
影响因子：
6.4
通讯作者：
Lidbetter, Thomas
中科院分区：
文献类型：
--
作者：
Angelopoulos, Spyros;Lidbetter, Thomas
我们研究了一个经典问题，即搜索者必须从一个根点开始定位一个隐藏点，也称为网络中的隐藏点。网络可以是有界的，也可以是无界的，从而推广了众所周知的设置，如线性搜索和星型搜索。我们区分了路径搜索和扩展搜索。路径搜索是指搜索者沿着一条连续的单位速度路径直到到达隐藏点。扩展搜索是指搜索者可以在任何时间点从之前到达的任何点重新开始搜索。前者一直是研究搜索游戏的常用范例，而后者是最近才出现的范例，可以模拟现实生活中的场景，如追捕逃犯、排雷或搜索和救援行动。我们寻求确定性和随机搜索策略，以最小化竞争比，即最坏情况下的发现时间比，除以从根到它的最短路径的长度。对于扩展搜索，我们证明了应用“注水”原则的简单搜索策略具有最优的确定性竞争比；相反，我们证明了即使在一个非常简单的三弧网络中，通过相当复杂的策略也能达到最优的随机竞争比。基于这一观察结果，我们提出并分析了一种扩展搜索策略，该策略是随机竞争比的5.4近似。我们的方法也适用于路径搜索，我们给出的策略是随机竞争比的5近似值，并且改进了从以前的工作中得出的策略。
We study the classic problem in which a Searcher must locate a hidden point, also called the Hider in a network, starting from a root point. The network may be either bounded or unbounded, thus generalizing well-known settings such as linear and star search. We distinguish between pathwise search, in which the Searcher follows a continuous unit-speed path until the Hider is reached, and expanding search, in which, at any point in time, the Searcher may restart from any previously reached point. The former has been the usual paradigm for studying search games, whereas the latter is a more recent paradigm that can model real-life settings such as hunting for a fugitive, demining a field, or search-and-rescue operations. We seek both deterministic and randomized search strategies that minimize the competitive ratio, namely the worst-case ratio of the Hider’s discovery time, divided by the length of the shortest path to it from the root. Concerning expanding search, we show that a simple search strategy that applies a “waterfilling” principle has optimal deterministic competitive ratio; in contrast, we show that the optimal randomized competitive ratio is attained by fairly complex strategies even in a very simple network of three arcs. Motivated by this observation, we present and analyze an expanding search strategy that is a 5 4-approximation of the randomized competitive ratio. Our approach is also applicable to pathwise search, for which we give a strategy that is a 5-approximation of the randomized competitive ratio, and which improves upon strategies derived from previous work.