Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing Minimum Cycle Bases in Weighted Partial 2-Trees in Linear Time   We present a linear time algorithm for computing an implicit linear space
representation of a minimum cycle basis (MCB) in weighted partial 2-trees,
i.e., graphs of treewidth two. The implicit representation can be made explicit
in a running time that is proportional to the size of the MCB.
  Our algorithm improves the result of Borradaile, Sankowski, and Wulff-Nilsen
[Min $st$-cut Oracle for Planar Graphs with Near-Linear Preprocessing Time,
FOCS 2010]---which computes for all planar graphs an implicit $O(n \log n)$
space representation of an MCB in $O(n \log^5 n)$ time---by a polylog factor
for the special case of partial 2-trees. Such an improvement was achieved
previously only for outerplanar graphs [Liu and Lu: Minimum Cycle Bases of
Weighted Outerplanar Graphs, IPL 110:970--974, 2010].

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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph