Generalized Red-Blue Circular Annulus Cover Problem
<|reference_start|>Generalized Red-Blue Circular Annulus Cover Problem: 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.<|reference_end|>
@article{maji2024generalized,
    title={Generalized Red-Blue Circular Annulus Cover Problem},
    author={Sukanya Maji, Supantha Pandit, Sanjib Sadhu},
    journal={arXiv preprint arXiv:2402.13767},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.13767},
    primaryClass={cs.CG}
}