Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Practical and Efficient Split Decomposition via Graph-Labelled Trees   Split decomposition of graphs was introduced by Cunningham (under the name
join decomposition) as a generalization of the modular decomposition. This
paper undertakes an investigation into the algorithmic properties of split
decomposition. We do so in the context of graph-labelled trees (GLTs), a new
combinatorial object designed to simplify its consideration. GLTs are used to
derive an incremental characterization of split decomposition, with a simple
combinatorial description, and to explore its properties with respect to
Lexicographic Breadth-First Search (LBFS). Applying the incremental
characterization to an LBFS ordering results in a split decomposition algorithm
that runs in time $O(n+m)\alpha(n+m)$, where $\alpha$ is the inverse Ackermann
function, whose value is smaller than 4 for any practical graph. Compared to
Dahlhaus' linear-time split decomposition algorithm [Dahlhaus'00], which does
not rely on an incremental construction, our algorithm is just as fast in all
but the asymptotic sense and full implementation details are given in this
paper. Also, our algorithm extends to circle graph recognition, whereas no such
extension is known for Dahlhaus' algorithm. The companion paper [Gioan et al.]
uses our algorithm to derive the first sub-quadratic circle graph recognition
algorithm.

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The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga