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Bicriteria Approximation Algorithms for Priority Matroid Median
The goal is to choose a subset $S \subseteq \mathcal{F}$ of facilities to minimize the $\sum_{i \in \mathcal{F}} f_i + \sum_{j \in \mathcal{C}} d(j, S)$ subject to two constraints: (i) $S$ is an independent set in $\mathcal{M}$ (that is $S \in \mathcal{I}$) and (ii) for each client $j$, its distance to an open facility is at most $r_j$ (that is, $d(j, S) \le r_j$).
Revisiting Priority $k$-Center: Fairness and Outliers
In the Priority $k$-Center problem, the input consists of a metric space $(X, d)$, an integer $k$, and for each point $v \in X$ a priority radius $r(v)$.
A new system-wide diversity measure for recommendations with efficient algorithms
(2) In the case of disjoint item categories and user types, we show that the resulting problems can be solved exactly in polynomial time, by a reduction to a minimum cost flow problem.
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