Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Single Exponential FPT Algorithm for Interval Vertex Deletion and
  Interval Completion Problem   Let G be an input graph with n vertices and m edges and let k be a fixed
parameter. We provide a single exponential FPT algorithm with running time
O(c^kn(n+m)), c= min {18,k} that turns graph G into an interval graph by
deleting at most k vertices from G. This solves an open problem posed by D.Marx
[19]. We also provide a single exponential FPT algorithm with running time
O(c^kn(n+m)), c= min {17,k} that turns G into an interval graph by adding at
most$k edges. The first FPT algorithm with run time O(k^{2k}n^3m) appeared in
STOC 2007 [24]. Our algorithm is the the first single exponential FPT algorithm
that improves the running time of the previous algorithm. The algorithms are
based on a structural decomposition of G into smaller subgraphs when G is free
from small interval graph obstructions. The decomposition allows us to manage
the search tree more efficiently.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th