Generalized Red-Blue Circular Annulus Cover Problem
CoRR(2024)
摘要
We study the Generalized Red-Blue Annulus Cover problem for two sets of
points, red (R) and blue (B), where each point p ∈ R∪ B is
associated with a positive penalty P(p). The red points have
non-covering penalties, and the blue points have covering penalties. The
objective is to compute a circular annulus A such that the value of
the function P(R^out) + P( B^in) is minimum, where
R^out⊆R is the set of red points not covered by A
and B^in⊆B is the set of blue points covered by 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.
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