Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Near-Optimal Approximate Shortest Paths and Transshipment in Distributed
  and Streaming Models   We present a method for solving the transshipment problem - also known as
uncapacitated minimum cost flow - up to a multiplicative error of $1 +
\varepsilon$ in undirected graphs with non-negative edge weights using a
tailored gradient descent algorithm. Using $\tilde{O}(\cdot)$ to hide
polylogarithmic factors in $n$ (the number of nodes in the graph), our gradient
descent algorithm takes $\tilde O(\varepsilon^{-2})$ iterations, and in each
iteration it solves an instance of the transshipment problem up to a
multiplicative error of $\operatorname{polylog} n$. In particular, this allows
us to perform a single iteration by computing a solution on a sparse spanner of
logarithmic stretch. Using a randomized rounding scheme, we can further extend
the method to finding approximate solutions for the single-source shortest
paths (SSSP) problem. As a consequence, we improve upon prior work by obtaining
the following results: (1) Broadcast CONGEST model: $(1 +
\varepsilon)$-approximate SSSP using $\tilde{O}((\sqrt{n} +
D)\varepsilon^{-3})$ rounds, where $ D $ is the (hop) diameter of the network.
(2) Broadcast congested clique model: $(1 + \varepsilon)$-approximate
transshipment and SSSP using $\tilde{O}(\varepsilon^{-2})$ rounds. (3)
Multipass streaming model: $(1 + \varepsilon)$-approximate transshipment and
SSSP using $\tilde{O}(n)$ space and $\tilde{O}(\varepsilon^{-2})$ passes. The
previously fastest SSSP algorithms for these models leverage sparse hop sets.
We bypass the hop set construction; computing a spanner is sufficient with our
method. The above bounds assume non-negative edge weights that are polynomially
bounded in $n$; for general non-negative weights, running times scale with the
logarithm of the maximum ratio between non-zero weights.

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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph