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- W2783005026 abstract "We consider the following problem: Preprocess a set $mathcal{S}$ of $n$ axis-parallel boxes in $mathbb{R}^d$ so that given a query of an axis-parallel box in $mathbb{R}^d$, the pairs of boxes of $mathcal{S}$ whose intersection intersects the query box can be reported efficiently. For the case that $d=2$, we present a data structure of size $O(nlog n)$ supporting $O(log n+k)$ query time, where $k$ is the size of the output. This improves the previously best known result by de Berg et al. which requires $O(log n+ klog n)$ query time using $O(nlog n)$ space. There has been no result known for this problem for higher dimensions, except that for $d=3$, the best known data structure supports $O(sqrt{n}log^2n+klog^2n)$ query time using $O(nsqrt {n}log n)$ space. For a constant $d>2$, we present a data structure supporting $O(n^{1-delta}log^{d-1} n + k text{ polylog } n)$ query time for any constant $1/dleqdelta<1$. The size of the data structure is $O(n^{delta d - 2delta + 1}log n)$." @default.
- W2783005026 created "2018-01-26" @default.
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- W2783005026 date "2018-01-23" @default.
- W2783005026 modified "2023-09-27" @default.
- W2783005026 title "Finding Pairwise Intersections of Rectangles in a Query Rectangle" @default.
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- W2783005026 hasPublicationYear "2018" @default.
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