The Search and Rescue Game on a Cycle
Thomas Lidbetter, Yifan Xie

TL;DR
This paper analyzes a search and rescue game on a cycle graph, providing solutions for single and multiple targets with success probabilities, including adaptive and non-adaptive search strategies, and extends to a continuous model.
Contribution
It offers the first complete solutions for search strategies on cycle graphs in both discrete and continuous settings, considering adaptive and non-adaptive approaches.
Findings
Exact solutions for single target with equal success probabilities.
Solutions for multiple targets with adaptive search strategies.
Approximate solutions for non-adaptive strategies in the continuous model.
Abstract
We consider a search and rescue game introduced recently by the first author. An immobile target or targets (for example, injured hikers) are hidden on a graph. The terrain is assumed to dangerous, so that when any given vertex of the graph is searched, there is a certain probability that the search will come to an end, otherwise with the complementary {\em success probability} the search can continue. A Searcher searches the graph with the aim of finding all the targets with maximum probability. Here, we focus on the game in the case that the graph is a cycle. In the case that there is only one target, we solve the game for equal success probabilities, and for a class of games with unequal success probabilities. For multiple targets and equal success probabilities, we give a solution for an adaptive Searcher and a solution in a special case for a non-adaptive Searcher. We also consider…
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Taxonomy
TopicsOptimization and Search Problems · Artificial Intelligence in Games · Robotic Path Planning Algorithms
