935 research outputs found
Shortest paths and load scaling in scale-free trees
The average node-to-node distance of scale-free graphs depends
logarithmically on N, the number of nodes, while the probability distribution
function (pdf) of the distances may take various forms. Here we analyze these
by considering mean-field arguments and by mapping the m=1 case of the
Barabasi-Albert model into a tree with a depth-dependent branching ratio. This
shows the origins of the average distance scaling and allows a demonstration of
why the distribution approaches a Gaussian in the limit of N large. The load
(betweenness), the number of shortest distance paths passing through any node,
is discussed in the tree presentation.Comment: 8 pages, 8 figures; v2: load calculations extende
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
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