Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Expected Complexity of Routing in $\Theta$ 6 and Half-$\Theta$ 6 Graphs   We study online routing algorithms on the $\Theta$6-graph and the
half-$\Theta$6-graph (which is equivalent to a variant of the Delaunay
triangulation). Given a source vertex s and a target vertex t in the
$\Theta$6-graph (resp. half-$\Theta$6-graph), there exists a deterministic
online routing algorithm that finds a path from s to t whose length is at most
2 st (resp. 2.89 st) which is optimal in the worst case [Bose et al., siam J.
on Computing, 44(6)]. We propose alternative, slightly simpler routing
algorithms that are optimal in the worst case and for which we provide an
analysis of the average routing ratio for the $\Theta$6-graph and
half-$\Theta$6-graph defined on a Poisson point process. For the
$\Theta$6-graph, our online routing algorithm has an expected routing ratio of
1.161 (when s and t random) and a maximum expected routing ratio of 1.22
(maximum for fixed s and t where all other points are random), much better than
the worst-case routing ratio of 2. For the half-$\Theta$6-graph, our memoryless
online routing algorithm has an expected routing ratio of 1.43 and a maximum
expected routing ratio of 1.58. Our online routing algorithm that uses a
constant amount of additional memory has an expected routing ratio of 1.34 and
a maximum expected routing ratio of 1.40. The additional memory is only used to
remember the coordinates of the starting point of the route. Both of these
algorithms have an expected routing ratio that is much better than their
worst-case routing ratio of 2.89.

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The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an