Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minor Excluded Network Families Admit Fast Distributed Algorithms   Distributed network optimization algorithms, such as minimum spanning tree,
minimum cut, and shortest path, are an active research area in distributed
computing. This paper presents a fast distributed algorithm for such problems
in the CONGEST model, on networks that exclude a fixed minor.
  On general graphs, many optimization problems, including the ones mentioned
above, require $\tilde\Omega(\sqrt n)$ rounds of communication in the CONGEST
model, even if the network graph has a much smaller diameter. Naturally, the
next step in algorithm design is to design efficient algorithms which bypass
this lower bound on a restricted class of graphs. Currently, the only known
method of doing so uses the low-congestion shortcut framework of Ghaffari and
Haeupler [SODA'16]. Building off of their work, this paper proves that excluded
minor graphs admit high-quality shortcuts, leading to an $\tilde O(D^2)$ round
algorithm for the aforementioned problems, where $D$ is the diameter of the
network graph. To work with excluded minor graph families, we utilize the Graph
Structure Theorem of Robertson and Seymour. To the best of our knowledge, this
is the first time the Graph Structure Theorem has been used for an algorithmic
result in the distributed setting.
  Even though the proof is involved, merely showing the existence of good
shortcuts is sufficient to obtain simple, efficient distributed algorithms. In
particular, the shortcut framework can efficiently construct near-optimal
shortcuts and then use them to solve the optimization problems. This, combined
with the very general family of excluded minor graphs, which includes most
other important graph classes, makes this result of significant interest.

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The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an