Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Constant Factor Approximation Algorithm for Boxicity of Circular Arc
  Graphs   Boxicity of a graph $G(V,E)$ is the minimum integer $k$ such that $G$ can be
represented as the intersection graph of $k$-dimensional axis parallel
rectangles in $\mathbf{R}^k$. Equivalently, it is the minimum number of
interval graphs on the vertex set $V$ such that the intersection of their edge
sets is $E$. It is known that boxicity cannot be approximated even for graph
classes like bipartite, co-bipartite and split graphs below $O(n^{0.5 -
\epsilon})$-factor, for any $\epsilon >0$ in polynomial time unless $NP=ZPP$.
Till date, there is no well known graph class of unbounded boxicity for which
even an $n^\epsilon$-factor approximation algorithm for computing boxicity is
known, for any $\epsilon <1$. In this paper, we study the boxicity problem on
Circular Arc graphs - intersection graphs of arcs of a circle. We give a
$(2+\frac{1}{k})$-factor polynomial time approximation algorithm for computing
the boxicity of any circular arc graph along with a corresponding box
representation, where $k \ge 1$ is its boxicity. For Normal Circular Arc(NCA)
graphs, with an NCA model given, this can be improved to an additive 2-factor
approximation algorithm. The time complexity of the algorithms to approximately
compute the boxicity is $O(mn+n^2)$ in both these cases and in $O(mn+kn^2)=
O(n^3)$ time we also get their corresponding box representations, where $n$ is
the number of vertices of the graph and $m$ is its number of edges. The
additive 2-factor algorithm directly works for any Proper Circular Arc graph,
since computing an NCA model for it can be done in polynomial time.

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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: eess