Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: LR-Drawings of Ordered Rooted Binary Trees and Near-Linear Area Drawings
  of Outerplanar Graphs   In this paper we study a family of algorithms, introduced by Chan [SODA 1999]
and called LR-algorithms, for drawing ordered rooted binary trees. In
particular, we are interested in constructing LR-drawings (that are drawings
obtained via LR-algorithms) with small width. Chan showed three different
LR-algorithms that achieve, for an ordered rooted binary tree with $n$ nodes,
width $O(n^{0.695})$, width $O(n^{0.5})$, and width $O(n^{0.48})$.
  We prove that, for every $n$-node ordered rooted binary tree, an LR-drawing
with minimum width can be constructed in $O(n^{1.48})$ time. Further, we show
an infinite family of $n$-node ordered rooted binary trees requiring
$\Omega(n^{0.418})$ width in any LR-drawing; no lower bound better than
$\Omega(\log n)$ was previously known. Finally, we present the results of an
experimental evaluation that allowed us to determine the minimum width of all
the ordered rooted binary trees with up to $451$ nodes.
  Our interest in LR-drawings is mainly motivated by a result of Di Battista
and Frati [Algorithmica 2009], who proved that $n$-vertex outerplanar graphs
have outerplanar straight-line drawings in $O(n^{1.48})$ area by means of a
drawing algorithm which resembles an LR-algorithm.
  We deepen the connection between LR-drawings and outerplanar straight-line
drawings by proving that, if $n$-node ordered rooted binary trees have
LR-drawings with $f(n)$ width, for any function $f(n)$, then $n$-vertex
outerplanar graphs have outerplanar straight-line drawings in $O(f(n))$ area.
  Finally, we exploit a structural decomposition for ordered rooted binary
trees introduced by Chan in order to prove that every $n$-vertex outerplanar
graph has an outerplanar straight-line drawing in $O(n\cdot 2^{\sqrt{2 \log_2
n}} \sqrt{\log n})$ area.

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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg