Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Streaming Algorithms for High Dimensional EMD and MST   We study streaming algorithms for two fundamental geometric problems:
computing the cost of a Minimum Spanning Tree (MST) of an $n$-point set $X
\subset \{1,2,\dots,\Delta\}^d$, and computing the Earth Mover Distance (EMD)
between two multi-sets $A,B \subset \{1,2,\dots,\Delta\}^d$ of size $n$. We
consider the turnstile model, where points can be added and removed. We give a
one-pass streaming algorithm for MST and a two-pass streaming algorithm for
EMD, both achieving an approximation factor of $\tilde{O}(\log n)$ and using
polylog$(n,d,\Delta)$-space only. Furthermore, our algorithm for EMD can be
compressed to a single pass with a small additive error. Previously, the best
known sublinear-space streaming algorithms for either problem achieved an
approximation of $O(\min\{ \log n , \log (\Delta d)\} \log n)$
[Andoni-Indyk-Krauthgamer '08, Backurs-Dong-Indyk-Razenshteyn-Wagner '20]. For
MST, we also prove that any constant space streaming algorithm can only achieve
an approximation of $\Omega(\log n)$, analogous to the $\Omega(\log n)$ lower
bound for EMD of [Andoni-Indyk-Krauthgamer '08].
  Our algorithms are based on an improved analysis of a recursive space
partitioning method known generically as the Quadtree. Specifically, we show
that the Quadtree achieves an $\tilde{O}(\log n)$ approximation for both EMD
and MST, improving on the $O(\min\{ \log n , \log (\Delta d)\} \log n)$
approximation of [Andoni-Indyk-Krauthgamer '08,
Backurs-Dong-Indyk-Razenshteyn-Wagner '20].

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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin