Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An efficient algorithm for the diameter of Cayley graphs generated by
  transposition trees   A problem of practical and theoretical interest is to determine or estimate
the diameter of various families of Cayley networks. The previously known
estimate for the diameter of Cayley graphs generated by transposition trees is
an upper bound given in the oft-cited paper of Akers and Krishnamurthy (1989).
In this work, we first assess the performance of their upper bound. We show
that for every $n$, there exists a tree on $n$ vertices, such that the
difference between the upper bound and the true diameter value is at least
$n-4$.
  Evaluating their upper bound takes time $\Omega(n!)$. In this paper, we
provide an algorithm that obtains an estimate of the diameter, but which
requires only time $O(n^2)$; furthermore, the value obtained by our algorithm
is less than or equal to the previously known diameter upper bound. Such an
improvement to polynomial time, while still performing at least as well as the
previous bound, is possible because our algorithm works directly with the
transposition tree on $n$ vertices and does not require examining any of the
permutations. We also provide a tree for which the value computed by our
algorithm is not necessarily unique, which is an important result because such
examples are quite rare. For all families of trees we have investigated so far,
each of the possible values computed by our algorithm happens to also be an
upper bound on the diameter.

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The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics