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T\\'oth, Kevin Balas","submitted_at":"2016-02-29T21:44:01Z","abstract_excerpt":"For points $p_1,\\ldots , p_n$ in the unit square $[0,1]^2$, an \\emph{anchored rectangle packing} consists of interior-disjoint axis-aligned empty rectangles $r_1,\\ldots , r_n\\subseteq [0,1]^2$ such that point $p_i$ is a corner of the rectangle $r_i$ (that is, $r_i$ is \\emph{anchored} at $p_i$) for $i=1,\\ldots, n$. We show that for every set of $n$ points in $[0,1]^2$, there is an anchored rectangle packing of area at least $7/12-O(1/n)$, and for every $n\\in \\mathbf{N}$, there are point sets for which the area of every anchored rectangle packing is at most $2/3$. 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