Back to Search
Start Over
Generalized Red-Blue Circular Annulus Cover Problem
- Publication Year :
- 2024
-
Abstract
- We study the Generalized Red-Blue Annulus Cover problem for two sets of points, red ($R$) and blue ($B$), where each point $p \in R\cup B$ is associated with a positive penalty ${\cal P}(p)$. The red points have non-covering penalties, and the blue points have covering penalties. The objective is to compute a circular annulus ${\cal A}$ such that the value of the function ${\cal P}({R}^{out})$ + ${\cal P}({ B}^{in})$ is minimum, where ${R}^{out} \subseteq {R}$ is the set of red points not covered by ${\cal A}$ and ${B}^{in} \subseteq {B}$ is the set of blue points covered by $\cal A$. We also study another version of this problem, where all the red points in $R$ and the minimum number of points in $B$ are covered by the circular annulus in two dimensions. We design polynomial-time algorithms for all such circular annulus problems.<br />Comment: 6 figures
- Subjects :
- Computer Science - Computational Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2402.13767
- Document Type :
- Working Paper