59 research outputs found
A multipath analysis of biswapped networks.
Biswapped networks of the form have recently been proposed as interconnection networks to be implemented as optical transpose interconnection systems. We provide a systematic construction of vertex-disjoint paths joining any two distinct vertices in , where is the connectivity of . In doing so, we obtain an upper bound of on the -diameter of , where is the diameter of and the -diameter. Suppose that we have a deterministic multipath source routing algorithm in an interconnection network that finds mutually vertex-disjoint paths in joining any distinct vertices and does this in time polynomial in , and (and independently of the number of vertices of ). Our constructions yield an analogous deterministic multipath source routing algorithm in the interconnection network that finds mutually vertex-disjoint paths joining any distinct vertices in so that these paths all have length bounded as above. Moreover, our algorithm has time complexity polynomial in , and . We also show that if is Hamiltonian then is Hamiltonian, and that if is a Cayley graph then is a Cayley graph
Constructing Two Edge-Disjoint Hamiltonian Cycles in Locally Twisted Cubes
The -dimensional hypercube network is one of the most popular
interconnection networks since it has simple structure and is easy to
implement. The -dimensional locally twisted cube, denoted by , an
important variation of the hypercube, has the same number of nodes and the same
number of connections per node as . One advantage of is that the
diameter is only about half of the diameter of . Recently, some
interesting properties of were investigated. In this paper, we
construct two edge-disjoint Hamiltonian cycles in the locally twisted cube
, for any integer . The presence of two edge-disjoint
Hamiltonian cycles provides an advantage when implementing algorithms that
require a ring structure by allowing message traffic to be spread evenly across
the locally twisted cube.Comment: 7 pages, 4 figure
Properties and Algorithms of the KCube Interconnection Networks
The KCube interconnection network was first introduced in 2010 in order to exploit the
good characteristics of two well-known interconnection networks, the hypercube and the
Kautz graph. KCube links up multiple processors in a communication network with high
density for a fixed degree. Since the KCube network is newly proposed, much study is
required to demonstrate its potential properties and algorithms that can be designed to solve
parallel computation problems.
In this thesis we introduce a new methodology to construct the KCube graph. Also,
with regard to this new approach, we will prove its Hamiltonicity in the general KC(m; k).
Moreover, we will find its connectivity followed by an optimal broadcasting scheme in
which a source node containing a message is to communicate it with all other processors.
In addition to KCube networks, we have studied a version of the routing problem in the
traditional hypercube, investigating this problem: whether there exists a shortest path in a
Qn between two nodes 0n and 1n, when the network is experiencing failed components. We
first conditionally discuss this problem when there is a constraint on the number of faulty
nodes, and subsequently introduce an algorithm to tackle the problem without restrictions
on the number of nodes
Fault-tolerant Designs in Lattice Networks on the Klein Bottle
In this note, we consider triangular, square and hexagonal lattices on the flat Klein bottle, and find subgraphs with the property that for any vertices there exists a longest path (cycle) avoiding all of them. This completes work previously done in other lattices
- …