Optimizing Visibility-based Search in Polygonal Domains
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915314203099136 |
|---|---|
| author | Huynh, Kien C. Mitchell, Joseph S. B. Nguyen, Linh Polishchuk, Valentin |
| author_facet | Huynh, Kien C. Mitchell, Joseph S. B. Nguyen, Linh Polishchuk, Valentin |
| contents | Given a geometric domain $P$, visibility-based search problems seek routes for one or more mobile agents ("watchmen") to move within $P$ in order to be able to see a portion (or all) of $P$, while optimizing objectives, such as the length(s) of the route(s), the size (e.g., area or volume) of the portion seen, the probability of detecting a target distributed within $P$ according to a prior distribution, etc. The classic watchman route problem seeks a shortest route for an observer, with omnidirectional vision, to see all of $P$. In this paper we study bicriteria optimization problems for a single mobile agent within a polygonal domain $P$ in the plane, with the criteria of route length and area seen. Specifically, we address the problem of computing a minimum length route that sees at least a specified area of $P$ (minimum length, for a given area quota). We also study the problem of computing a length-constrained route that sees as much area as possible. We provide hardness results and approximation algorithms. In particular, for a simple polygon $P$ we provide the first fully polynomial-time approximation scheme for the problem of computing a shortest route seeing an area quota, as well as a (slightly more efficient) polynomial dual approximation. We also consider polygonal domains $P$ (with holes) and the special case of a planar domain consisting of a union of lines. Our results yield the first approximation algorithms for computing a time-optimal search route in $P$ to guarantee some specified probability of detection of a static target within $P$, randomly distributed in $P$ according to a given prior distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimizing Visibility-based Search in Polygonal Domains Huynh, Kien C. Mitchell, Joseph S. B. Nguyen, Linh Polishchuk, Valentin Computational Geometry F.2.2; I.3.5 Given a geometric domain $P$, visibility-based search problems seek routes for one or more mobile agents ("watchmen") to move within $P$ in order to be able to see a portion (or all) of $P$, while optimizing objectives, such as the length(s) of the route(s), the size (e.g., area or volume) of the portion seen, the probability of detecting a target distributed within $P$ according to a prior distribution, etc. The classic watchman route problem seeks a shortest route for an observer, with omnidirectional vision, to see all of $P$. In this paper we study bicriteria optimization problems for a single mobile agent within a polygonal domain $P$ in the plane, with the criteria of route length and area seen. Specifically, we address the problem of computing a minimum length route that sees at least a specified area of $P$ (minimum length, for a given area quota). We also study the problem of computing a length-constrained route that sees as much area as possible. We provide hardness results and approximation algorithms. In particular, for a simple polygon $P$ we provide the first fully polynomial-time approximation scheme for the problem of computing a shortest route seeing an area quota, as well as a (slightly more efficient) polynomial dual approximation. We also consider polygonal domains $P$ (with holes) and the special case of a planar domain consisting of a union of lines. Our results yield the first approximation algorithms for computing a time-optimal search route in $P$ to guarantee some specified probability of detection of a static target within $P$, randomly distributed in $P$ according to a given prior distribution. |
| title | Optimizing Visibility-based Search in Polygonal Domains |
| topic | Computational Geometry F.2.2; I.3.5 |
| url | https://arxiv.org/abs/2402.05420 |