5,390 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
Forwarding and optical indices of 4-regular circulant networks
An all-to-all routing in a graph is a set of oriented paths of , with
exactly one path for each ordered pair of vertices. The load of an edge under
an all-to-all routing is the number of times it is used (in either
direction) by paths of , and the maximum load of an edge is denoted by
. The edge-forwarding index is the minimum of
over all possible all-to-all routings , and the arc-forwarding index
is defined similarly by taking direction into
consideration, where an arc is an ordered pair of adjacent vertices. Denote by
the minimum number of colours required to colour the paths of such
that any two paths having an edge in common receive distinct colours. The
optical index is defined to be the minimum of over all possible
, and the directed optical index is defined
similarly by requiring that any two paths having an arc in common receive
distinct colours. In this paper we obtain lower and upper bounds on these four
invariants for -regular circulant graphs with connection set , . We give approximation algorithms with performance ratio a
small constant for the corresponding forwarding index and routing and
wavelength assignment problems for some families of -regular circulant
graphs.Comment: 19 pages, no figure in Journal of Discrete Algorithms 201
Decentralized Routing on Spatial Networks with Stochastic Edge Weights
We investigate algorithms to find short paths in spatial networks with
stochastic edge weights. Our formulation of the problem of finding short paths
differs from traditional formulations because we specifically do not make two
of the usual simplifying assumptions: (1) we allow edge weights to be
stochastic rather than deterministic; and (2) we do not assume that global
knowledge of a network is available. We develop a decentralized routing
algorithm that provides en route guidance for travelers on a spatial network
with stochastic edge weights without the need to rely on global knowledge about
the network. To guide a traveler, our algorithm uses an estimation function
that evaluates cumulative arrival probability distributions based on distances
between pairs of nodes. The estimation function carries a notion of proximity
between nodes and thereby enables routing without global knowledge. In testing
our decentralized algorithm, we define a criterion that allows one to
discriminate among arrival probability distributions, and we test our algorithm
and this criterion using both synthetic and real networks.Comment: 10 pages, 9 figures (some with multiple parts
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