Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Spanning and Routing Ratio of Directed Theta-Four   We present a routing algorithm for the directed $\Theta_4$-graph, here
denoted as the $\overrightarrow{\Theta_4}}$-graph, that computes a path between
any two vertices $s$ and $t$ having length at most $17$ times the Euclidean
distance between $s$ and $t$. To compute this path, at each step, the algorithm
only uses knowledge of the location of the current vertex, its (at most four)
outgoing edges, the destination vertex, and one additional bit of information
in order to determine the next edge to follow. This provides the first known
online, local, competitive routing algorithm with constant routing ratio for
the $\Theta_4$-graph, as well as improving the best known upper bound on the
spanning ratio of these graphs from $237$ to $17$. We also show that without
this additional bit of information, the routing ratio increases to $\sqrt{290}
\approx 17.03$.

24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin