Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing Kantorovich-Wasserstein Distances on $d$-dimensional
  histograms using $(d+1)$-partite graphs   This paper presents a novel method to compute the exact
Kantorovich-Wasserstein distance between a pair of $d$-dimensional histograms
having $n$ bins each. We prove that this problem is equivalent to an
uncapacitated minimum cost flow problem on a $(d+1)$-partite graph with
$(d+1)n$ nodes and $dn^{\frac{d+1}{d}}$ arcs, whenever the cost is separable
along the principal $d$-dimensional directions. We show numerically the
benefits of our approach by computing the Kantorovich-Wasserstein distance of
order 2 among two sets of instances: gray scale images and $d$-dimensional
biomedical histograms. On these types of instances, our approach is competitive
with state-of-the-art optimal transport algorithms.

27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int