Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Fault Tolerance and Hamiltonicity of the Optical Transpose
  Interconnection System of Non-Hamiltonian Base Graphs   Hamiltonicity is an important property in parallel and distributed
computation. Existence of Hamiltonian cycle allows efficient emulation of
distributed algorithms on a network wherever such algorithm exists for
linear-array and ring, and can ensure deadlock freedom in some routing
algorithms in hierarchical interconnection networks. Hamiltonicity can also be
used for construction of independent spanning tree and leads to designing fault
tolerant protocols. Optical Transpose Interconnection Systems or OTIS (also
referred to as two-level swapped network) is a widely studied interconnection
network topology which is popular due to high degree of scalability,
regularity, modularity and package ability. Surprisingly, to our knowledge,
only one strong result is known regarding Hamiltonicity of OTIS - showing that
OTIS graph built of Hamiltonian base graphs are Hamiltonian. In this work we
consider Hamiltonicity of OTIS networks, built on Non-Hamiltonian base and
answer some important questions. First, we prove that Hamiltonicity of base
graph is not a necessary condition for the OTIS to be Hamiltonian. We present
an infinite family of Hamiltonian OTIS graphs composed on Non-Hamiltonian base
graphs. We further show that, it is not sufficient for the base graph to have
Hamiltonian path for the OTIS constructed on it to be Hamiltonian. We give
constructive proof of Hamiltonicity for a large family of Butterfly-OTIS. This
proof leads to an alternate efficient algorithm for independent spanning trees
construction on this class of OTIS graphs. Our algorithm is linear in the
number of vertices as opposed to the generalized algorithm, which is linear in
the number of edges of the graph.

22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph