16,055 research outputs found
Conditional Reliability in Uncertain Graphs
Network reliability is a well-studied problem that requires to measure the
probability that a target node is reachable from a source node in a
probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned
a probability of existence. Many approaches and problem variants have been
considered in the literature, all assuming that edge-existence probabilities
are fixed. Nevertheless, in real-world graphs, edge probabilities typically
depend on external conditions. In metabolic networks a protein can be converted
into another protein with some probability depending on the presence of certain
enzymes. In social influence networks the probability that a tweet of some user
will be re-tweeted by her followers depends on whether the tweet contains
specific hashtags. In transportation networks the probability that a network
segment will work properly or not might depend on external conditions such as
weather or time of the day. In this paper we overcome this limitation and focus
on conditional reliability, that is assessing reliability when edge-existence
probabilities depend on a set of conditions. In particular, we study the
problem of determining the k conditions that maximize the reliability between
two nodes. We deeply characterize our problem and show that, even employing
polynomial-time reliability-estimation methods, it is NP-hard, does not admit
any PTAS, and the underlying objective function is non-submodular. We then
devise a practical method that targets both accuracy and efficiency. We also
study natural generalizations of the problem with multiple source and target
nodes. An extensive empirical evaluation on several large, real-life graphs
demonstrates effectiveness and scalability of the proposed methods.Comment: 14 pages, 13 figure
On the Quality of Wireless Network Connectivity
Despite intensive research in the area of network connectivity, there is an
important category of problems that remain unsolved: how to measure the quality
of connectivity of a wireless multi-hop network which has a realistic number of
nodes, not necessarily large enough to warrant the use of asymptotic analysis,
and has unreliable connections, reflecting the inherent unreliable
characteristics of wireless communications? The quality of connectivity
measures how easily and reliably a packet sent by a node can reach another
node. It complements the use of \emph{capacity} to measure the quality of a
network in saturated traffic scenarios and provides a native measure of the
quality of (end-to-end) network connections. In this paper, we explore the use
of probabilistic connectivity matrix as a possible tool to measure the quality
of network connectivity. Some interesting properties of the probabilistic
connectivity matrix and their connections to the quality of connectivity are
demonstrated. We argue that the largest eigenvalue of the probabilistic
connectivity matrix can serve as a good measure of the quality of network
connectivity.Comment: submitted to IEEE INFOCOM 201
Injecting Uncertainty in Graphs for Identity Obfuscation
Data collected nowadays by social-networking applications create fascinating
opportunities for building novel services, as well as expanding our
understanding about social structures and their dynamics. Unfortunately,
publishing social-network graphs is considered an ill-advised practice due to
privacy concerns. To alleviate this problem, several anonymization methods have
been proposed, aiming at reducing the risk of a privacy breach on the published
data, while still allowing to analyze them and draw relevant conclusions. In
this paper we introduce a new anonymization approach that is based on injecting
uncertainty in social graphs and publishing the resulting uncertain graphs.
While existing approaches obfuscate graph data by adding or removing edges
entirely, we propose using a finer-grained perturbation that adds or removes
edges partially: this way we can achieve the same desired level of obfuscation
with smaller changes in the data, thus maintaining higher utility. Our
experiments on real-world networks confirm that at the same level of identity
obfuscation our method provides higher usefulness than existing randomized
methods that publish standard graphs.Comment: VLDB201
Visualizing Sensor Network Coverage with Location Uncertainty
We present an interactive visualization system for exploring the coverage in
sensor networks with uncertain sensor locations. We consider a simple case of
uncertainty where the location of each sensor is confined to a discrete number
of points sampled uniformly at random from a region with a fixed radius.
Employing techniques from topological data analysis, we model and visualize
network coverage by quantifying the uncertainty defined on its simplicial
complex representations. We demonstrate the capabilities and effectiveness of
our tool via the exploration of randomly distributed sensor networks
The Topology ToolKit
This system paper presents the Topology ToolKit (TTK), a software platform
designed for topological data analysis in scientific visualization. TTK
provides a unified, generic, efficient, and robust implementation of key
algorithms for the topological analysis of scalar data, including: critical
points, integral lines, persistence diagrams, persistence curves, merge trees,
contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots,
Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due
to a tight integration with ParaView. It is also easily accessible to
developers through a variety of bindings (Python, VTK/C++) for fast prototyping
or through direct, dependence-free, C++, to ease integration into pre-existing
complex systems. While developing TTK, we faced several algorithmic and
software engineering challenges, which we document in this paper. In
particular, we present an algorithm for the construction of a discrete gradient
that complies to the critical points extracted in the piecewise-linear setting.
This algorithm guarantees a combinatorial consistency across the topological
abstractions supported by TTK, and importantly, a unified implementation of
topological data simplification for multi-scale exploration and analysis. We
also present a cached triangulation data structure, that supports time
efficient and generic traversals, which self-adjusts its memory usage on demand
for input simplicial meshes and which implicitly emulates a triangulation for
regular grids with no memory overhead. Finally, we describe an original
software architecture, which guarantees memory efficient and direct accesses to
TTK features, while still allowing for researchers powerful and easy bindings
and extensions. TTK is open source (BSD license) and its code, online
documentation and video tutorials are available on TTK's website
Graph Summarization
The continuous and rapid growth of highly interconnected datasets, which are
both voluminous and complex, calls for the development of adequate processing
and analytical techniques. One method for condensing and simplifying such
datasets is graph summarization. It denotes a series of application-specific
algorithms designed to transform graphs into more compact representations while
preserving structural patterns, query answers, or specific property
distributions. As this problem is common to several areas studying graph
topologies, different approaches, such as clustering, compression, sampling, or
influence detection, have been proposed, primarily based on statistical and
optimization methods. The focus of our chapter is to pinpoint the main graph
summarization methods, but especially to focus on the most recent approaches
and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie
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