4,031 research outputs found
Distance Oracles for Time-Dependent Networks
We present the first approximate distance oracle for sparse directed networks
with time-dependent arc-travel-times determined by continuous, piecewise
linear, positive functions possessing the FIFO property.
Our approach precomputes approximate distance summaries from
selected landmark vertices to all other vertices in the network. Our oracle
uses subquadratic space and time preprocessing, and provides two sublinear-time
query algorithms that deliver constant and approximate
shortest-travel-times, respectively, for arbitrary origin-destination pairs in
the network, for any constant . Our oracle is based only on
the sparsity of the network, along with two quite natural assumptions about
travel-time functions which allow the smooth transition towards asymmetric and
time-dependent distance metrics.Comment: A preliminary version appeared as Technical Report ECOMPASS-TR-025 of
EU funded research project eCOMPASS (http://www.ecompass-project.eu/). An
extended abstract also appeared in the 41st International Colloquium on
Automata, Languages, and Programming (ICALP 2014, track-A
When is a Network a Network? Multi-Order Graphical Model Selection in Pathways and Temporal Networks
We introduce a framework for the modeling of sequential data capturing
pathways of varying lengths observed in a network. Such data are important,
e.g., when studying click streams in information networks, travel patterns in
transportation systems, information cascades in social networks, biological
pathways or time-stamped social interactions. While it is common to apply graph
analytics and network analysis to such data, recent works have shown that
temporal correlations can invalidate the results of such methods. This raises a
fundamental question: when is a network abstraction of sequential data
justified? Addressing this open question, we propose a framework which combines
Markov chains of multiple, higher orders into a multi-layer graphical model
that captures temporal correlations in pathways at multiple length scales
simultaneously. We develop a model selection technique to infer the optimal
number of layers of such a model and show that it outperforms previously used
Markov order detection techniques. An application to eight real-world data sets
on pathways and temporal networks shows that it allows to infer graphical
models which capture both topological and temporal characteristics of such
data. Our work highlights fallacies of network abstractions and provides a
principled answer to the open question when they are justified. Generalizing
network representations to multi-order graphical models, it opens perspectives
for new data mining and knowledge discovery algorithms.Comment: 10 pages, 4 figures, 1 table, companion python package pathpy
available on gitHu
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