3,183 research outputs found
Sustaining the Internet with Hyperbolic Mapping
The Internet infrastructure is severely stressed. Rapidly growing overheads
associated with the primary function of the Internet---routing information
packets between any two computers in the world---cause concerns among Internet
experts that the existing Internet routing architecture may not sustain even
another decade. Here we present a method to map the Internet to a hyperbolic
space. Guided with the constructed map, which we release with this paper,
Internet routing exhibits scaling properties close to theoretically best
possible, thus resolving serious scaling limitations that the Internet faces
today. Besides this immediate practical viability, our network mapping method
can provide a different perspective on the community structure in complex
networks
Sampling of graph signals via randomized local aggregations
Sampling of signals defined over the nodes of a graph is one of the crucial
problems in graph signal processing. While in classical signal processing
sampling is a well defined operation, when we consider a graph signal many new
challenges arise and defining an efficient sampling strategy is not
straightforward. Recently, several works have addressed this problem. The most
common techniques select a subset of nodes to reconstruct the entire signal.
However, such methods often require the knowledge of the signal support and the
computation of the sparsity basis before sampling. Instead, in this paper we
propose a new approach to this issue. We introduce a novel technique that
combines localized sampling with compressed sensing. We first choose a subset
of nodes and then, for each node of the subset, we compute random linear
combinations of signal coefficients localized at the node itself and its
neighborhood. The proposed method provides theoretical guarantees in terms of
reconstruction and stability to noise for any graph and any orthonormal basis,
even when the support is not known.Comment: IEEE Transactions on Signal and Information Processing over Networks,
201
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