Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Fast Heuristic Algorithms and Post-Processing Techniques to Design
  Large and Low-Cost Communication Networks   It is challenging to design large and low-cost communication networks. In
this paper, we formulate this challenge as the prize-collecting Steiner Tree
Problem (PCSTP). The objective is to minimize the costs of transmission routes
and the disconnected monetary or informational profits. Initially, we note that
the PCSTP is MAX SNP-hard. Then, we propose some post-processing techniques to
improve suboptimal solutions to PCSTP. Based on these techniques, we propose
two fast heuristic algorithms: the first one is a quasilinear time heuristic
algorithm that is faster and consumes less memory than other algorithms; and
the second one is an improvement of a stateof-the-art polynomial time heuristic
algorithm that can find high-quality solutions at a speed that is only inferior
to the first one. We demonstrate the competitiveness of our heuristic
algorithms by comparing them with the state-of-the-art ones on the largest
existing benchmark instances (169 800 vertices and 338 551 edges). Moreover, we
generate new instances that are even larger (1 000 000 vertices and 10 000 000
edges) to further demonstrate their advantages in large networks. The
state-ofthe-art algorithms are too slow to find high-quality solutions for
instances of this size, whereas our new heuristic algorithms can do this in
around 6 to 45s on a personal computer. Ultimately, we apply our
post-processing techniques to update the bestknown solution for a notoriously
difficult benchmark instance to show that they can improve near-optimal
solutions to PCSTP. In conclusion, we demonstrate the usefulness of our
heuristic algorithms and post-processing techniques for designing large and
low-cost communication networks.

12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: quant-ph