Partial Interval Multicover Is NP-Complete Even for Unit Intervals
For a interval family $\calI$, a point set $X\subseteq\mathbb R$, demands $d:X\to\Z_{\ge0}$, and $p\in\Z_{\ge0}$, partial interval multicover asks for a subfamily $S\subseteq\calI$ minimizing $|S|$ subject to $$ |\{x\in X:\dep_S(x)\ge d(x)\}|\ge p, \qquad \dep_S(x)=|\{I\in S:x\in I\}|. $$ We prove that the unweighted decision problem is NP-complete even for unit intervals, answering the open question in~\cite{Li2026}.
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