37,640 research outputs found
Symmetric Interconnection Networks from Cubic Crystal Lattices
Torus networks of moderate degree have been widely used in the supercomputer
industry. Tori are superb when used for executing applications that require
near-neighbor communications. Nevertheless, they are not so good when dealing
with global communications. Hence, typical 3D implementations have evolved to
5D networks, among other reasons, to reduce network distances. Most of these
big systems are mixed-radix tori which are not the best option for minimizing
distances and efficiently using network resources. This paper is focused on
improving the topological properties of these networks.
By using integral matrices to deal with Cayley graphs over Abelian groups, we
have been able to propose and analyze a family of high-dimensional grid-based
interconnection networks. As they are built over -dimensional grids that
induce a regular tiling of the space, these topologies have been denoted
\textsl{lattice graphs}. We will focus on cubic crystal lattices for modeling
symmetric 3D networks. Other higher dimensional networks can be composed over
these graphs, as illustrated in this research. Easy network partitioning can
also take advantage of this network composition operation. Minimal routing
algorithms are also provided for these new topologies. Finally, some practical
issues such as implementability and preliminary performance evaluations have
been addressed
Batch kernel SOM and related Laplacian methods for social network analysis
Large graphs are natural mathematical models for describing the structure of
the data in a wide variety of fields, such as web mining, social networks,
information retrieval, biological networks, etc. For all these applications,
automatic tools are required to get a synthetic view of the graph and to reach
a good understanding of the underlying problem. In particular, discovering
groups of tightly connected vertices and understanding the relations between
those groups is very important in practice. This paper shows how a kernel
version of the batch Self Organizing Map can be used to achieve these goals via
kernels derived from the Laplacian matrix of the graph, especially when it is
used in conjunction with more classical methods based on the spectral analysis
of the graph. The proposed method is used to explore the structure of a
medieval social network modeled through a weighted graph that has been directly
built from a large corpus of agrarian contracts
New results for the degree/diameter problem
The results of computer searches for large graphs with given (small) degree
and diameter are presented. The new graphs are Cayley graphs of semidirect
products of cyclic groups and related groups. One fundamental use of our
``dense graphs'' is in the design of efficient communication network
topologies.Comment: 15 page
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