Multi-Agent Search-Type Problems on Polygons
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911935585320960 |
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| author | Georgiou, Konstantinos Jones, Caleb Lucier, Jesse |
| author_facet | Georgiou, Konstantinos Jones, Caleb Lucier, Jesse |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19495 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-Agent Search-Type Problems on Polygons Georgiou, Konstantinos Jones, Caleb Lucier, Jesse Discrete Mathematics 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. |
| title | Multi-Agent Search-Type Problems on Polygons |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2406.19495 |