1,889 research outputs found
An Axiomatic Approach to Routing
Information delivery in a network of agents is a key issue for large, complex
systems that need to do so in a predictable, efficient manner. The delivery of
information in such multi-agent systems is typically implemented through
routing protocols that determine how information flows through the network.
Different routing protocols exist each with its own benefits, but it is
generally unclear which properties can be successfully combined within a given
algorithm. We approach this problem from the axiomatic point of view, i.e., we
try to establish what are the properties we would seek to see in such a system,
and examine the different properties which uniquely define common routing
algorithms used today.
We examine several desirable properties, such as robustness, which ensures
adding nodes and edges does not change the routing in a radical, unpredictable
ways; and properties that depend on the operating environment, such as an
"economic model", where nodes choose their paths based on the cost they are
charged to pass information to the next node. We proceed to fully characterize
minimal spanning tree, shortest path, and weakest link routing algorithms,
showing a tight set of axioms for each.Comment: In Proceedings TARK 2015, arXiv:1606.0729
Persistent Homology of Coarse Grained State Space Networks
This work is dedicated to the topological analysis of complex transitional
networks for dynamic state detection. Transitional networks are formed from
time series data and they leverage graph theory tools to reveal information
about the underlying dynamic system. However, traditional tools can fail to
summarize the complex topology present in such graphs. In this work, we
leverage persistent homology from topological data analysis to study the
structure of these networks. We contrast dynamic state detection from time
series using CGSSN and TDA to two state of the art approaches: Ordinal
Partition Networks (OPNs) combined with TDA, and the standard application of
persistent homology to the time-delay embedding of the signal. We show that the
CGSSN captures rich information about the dynamic state of the underlying
dynamical system as evidenced by a significant improvement in dynamic state
detection and noise robustness in comparison to OPNs. We also show that because
the computational time of CGSSN is not linearly dependent on the signal's
length, it is more computationally efficient than applying TDA to the
time-delay embedding of the time series
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