3,190 research outputs found
Ricci Curvature of the Internet Topology
Analysis of Internet topologies has shown that the Internet topology has
negative curvature, measured by Gromov's "thin triangle condition", which is
tightly related to core congestion and route reliability. In this work we
analyze the discrete Ricci curvature of the Internet, defined by Ollivier, Lin,
etc. Ricci curvature measures whether local distances diverge or converge. It
is a more local measure which allows us to understand the distribution of
curvatures in the network. We show by various Internet data sets that the
distribution of Ricci cuvature is spread out, suggesting the network topology
to be non-homogenous. We also show that the Ricci curvature has interesting
connections to both local measures such as node degree and clustering
coefficient, global measures such as betweenness centrality and network
connectivity, as well as auxilary attributes such as geographical distances.
These observations add to the richness of geometric structures in complex
network theory.Comment: 9 pages, 16 figures. To be appear on INFOCOM 201
Hyperbolic Interaction Model For Hierarchical Multi-Label Classification
Different from the traditional classification tasks which assume mutual
exclusion of labels, hierarchical multi-label classification (HMLC) aims to
assign multiple labels to every instance with the labels organized under
hierarchical relations. Besides the labels, since linguistic ontologies are
intrinsic hierarchies, the conceptual relations between words can also form
hierarchical structures. Thus it can be a challenge to learn mappings from word
hierarchies to label hierarchies. We propose to model the word and label
hierarchies by embedding them jointly in the hyperbolic space. The main reason
is that the tree-likeness of the hyperbolic space matches the complexity of
symbolic data with hierarchical structures. A new Hyperbolic Interaction Model
(HyperIM) is designed to learn the label-aware document representations and
make predictions for HMLC. Extensive experiments are conducted on three
benchmark datasets. The results have demonstrated that the new model can
realistically capture the complex data structures and further improve the
performance for HMLC comparing with the state-of-the-art methods. To facilitate
future research, our code is publicly available
Greedy Forwarding in Dynamic Scale-Free Networks Embedded in Hyperbolic Metric Spaces
We show that complex (scale-free) network topologies naturally emerge from
hyperbolic metric spaces. Hyperbolic geometry facilitates maximally efficient
greedy forwarding in these networks. Greedy forwarding is topology-oblivious.
Nevertheless, greedy packets find their destinations with 100% probability
following almost optimal shortest paths. This remarkable efficiency sustains
even in highly dynamic networks. Our findings suggest that forwarding
information through complex networks, such as the Internet, is possible without
the overhead of existing routing protocols, and may also find practical
applications in overlay networks for tasks such as application-level routing,
information sharing, and data distribution
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