We study the classic problem of searching for a hidden target in the line and the $m$-ray star, in a setting in which the searcher has some prediction on the hider's position. We first focus on the main metric for comparing search strategies under predictions; namely, we give positive and negative results on the consistency-robustness tradeoff, where the performance of the strategy is evaluated at extreme situations in which the prediction is either error-free, or adversarially generated, respectively. For the line, we show tight bounds concerning this tradeoff, under the untrusted advice model, in which the prediction is in the form of a $k$-bit string which encodes the responses to $k$ binary queries. For the star, we give tight, and near-tight tradeoffs in the positional and the directional models, in which the prediction is related to the position of the target within the star, and to the ray on which the target hides, respectively. Last, for all three prediction models, we show how to generalize our study to a setting in which the performance of the strategy is evaluated as a function of the searcher's desired tolerance to prediction errors, both in terms of positive and inapproximability results.

翻译：我们研究在直线和$m$射线星形结构中搜索隐藏目标的经典问题，其中搜索者拥有关于隐藏者位置的某些预测。我们首先关注在预测下比较搜索策略的主要度量；即，我们给出关于一致性-鲁棒性权衡的正反结果，其中策略的性能在预测无误差或对抗性生成的极端情况下分别评估。对于直线，我们在不可信建议模型下展示了关于此权衡的紧致边界，其中预测形式为编码$k$个二进制查询响应的$k$位字符串。对于星形，我们在位置模型和方向模型中分别给出紧致和近乎紧致的权衡，其中预测分别涉及目标在星形结构内的位置以及目标隐藏所在射线。最后，针对所有三种预测模型，我们展示如何将研究推广到策略性能作为搜索者对预测误差期望容限的函数进行评估的情形，涵盖正面结果和不可近似性结果。