We present several advancements in search-type problems for fleets of mobile agents operating in two dimensions under the wireless model. Potential hidden target locations are equidistant from a central point, forming either a disk (infinite possible locations) or regular polygons (finite possible locations). Building on the foundational disk evacuation problem, the disk priority evacuation problem with $k$ Servants, and the disk $w$-weighted search problem, we make improvements on several fronts. First we establish new upper and lower bounds for the $n$-gon priority evacuation problem with $1$ Servant for $n \leq 13$, and for $n_k$-gons with $k=2, 3, 4$ Servants, where $n_2 \leq 11$, $n_3 \leq 9$, and $n_4 \leq 10$, offering tight or nearly tight bounds. The only previous results known were a tight upper bound for $k=1$ and $n=6$ and lower bounds for $k=1$ and $n \leq 9$. Second, our work improves the best lower bound known for the disk priority evacuation problem with $k=1$ Servant from $4.46798$ to $4.64666$ and for $k=2$ Servants from $3.6307$ to $3.65332$. Third, we improve the best lower bounds known for the disk $w$-weighted group search problem, significantly reducing the gap between the best upper and lower bounds for $w$ values where the gap was largest. These improvements are based on nearly tight upper and lower bounds for the $11$-gon and $12$-gon $w$-weighted evacuation problems, while previous analyses were limited only to lower bounds and only to $7$-gons.

翻译：我们在无线模型下运行的二维移动智能体群组的搜索型问题上取得了若干进展。潜在的隐藏目标位置与中心点等距，形成一个圆盘（无限可能位置）或正多边形（有限可能位置）。基于基础的圆盘撤离问题、带 $k$ 个从属智能体的圆盘优先级撤离问题以及圆盘 $w$-加权搜索问题，我们在多个方面做出了改进。首先，我们为 $n \leq 13$ 时的带 $1$ 个从属智能体的 $n$ 边形优先级撤离问题，以及为 $k=2, 3, 4$ 个从属智能体时的 $n_k$ 边形问题建立了新的上界和下界，其中 $n_2 \leq 11$，$n_3 \leq 9$，$n_4 \leq 10$，提供了紧或近乎紧的界。此前已知的唯一结果是 $k=1$ 且 $n=6$ 时的紧上界，以及 $k=1$ 且 $n \leq 9$ 时的下界。其次，我们的工作将带 $k=1$ 个从属智能体的圆盘优先级撤离问题的最佳已知下界从 $4.46798$ 改进至 $4.64666$，并将带 $k=2$ 个从属智能体的该问题最佳已知下界从 $3.6307$ 改进至 $3.65332$。第三，我们改进了圆盘 $w$-加权群组搜索问题的最佳已知下界，显著缩小了在 $w$ 值上界与下界之间差距最大的情况下的差距。这些改进基于对 $11$ 边形和 $12$ 边形 $w$-加权撤离问题近乎紧的上界和下界分析，而先前的分析仅限于下界且仅针对 $7$ 边形。