770 research outputs found
Computing maximal cliques in link streams
Abstract A link stream is a collection of triplets (t, u, v) indicating that an interaction occurred between u and v at time t. We generalize the classical notion of cliques in graphs to such link streams: for a given â, a â-clique is a set of nodes and a time interval such that all pairs of nodes in this set interact at least once during each sub-interval of duration â. We propose an algorithm to enumerate all maximal (in terms of nodes or time interval) cliques of a link stream, and illustrate its practical relevance on a real-world contact trace
Enumerating maximal cliques in link streams with durations
Link streams model interactions over time, and a clique in a link stream is
defined as a set of nodes and a time interval such that all pairs of nodes in
this set interact permanently during this time interval. This notion was
introduced recently in the case where interactions are instantaneous. We
generalize it to the case of interactions with durations and show that the
instantaneous case actually is a particular case of the case with durations. We
propose an algorithm to detect maximal cliques that improves our previous one
for instantaneous link streams, and performs better than the state of the art
algorithms in several cases of interest
Discovering Patterns of Interest in IP Traffic Using Cliques in Bipartite Link Streams
Studying IP traffic is crucial for many applications. We focus here on the
detection of (structurally and temporally) dense sequences of interactions,
that may indicate botnets or coordinated network scans. More precisely, we
model a MAWI capture of IP traffic as a link streams, i.e. a sequence of
interactions meaning that devices and exchanged
packets from time to time . This traffic is captured on a single
router and so has a bipartite structure: links occur only between nodes in two
disjoint sets. We design a method for finding interesting bipartite cliques in
such link streams, i.e. two sets of nodes and a time interval such that all
nodes in the first set are linked to all nodes in the second set throughout the
time interval. We then explore the bipartite cliques present in the considered
trace. Comparison with the MAWILab classification of anomalous IP addresses
shows that the found cliques succeed in detecting anomalous network activity
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
LSCPM: communities in massive real-world Link Streams by Clique Percolation Method
Community detection is a popular approach to understand the organization of
interactions in static networks. For that purpose, the Clique Percolation
Method (CPM), which involves the percolation of k-cliques, is a well-studied
technique that offers several advantages. Besides, studying interactions that
occur over time is useful in various contexts, which can be modeled by the link
stream formalism. The Dynamic Clique Percolation Method (DCPM) has been
proposed for extending CPM to temporal networks.
However, existing implementations are unable to handle massive datasets. We
present a novel algorithm that adapts CPM to link streams, which has the
advantage that it allows us to speed up the computation time with respect to
the existing DCPM method. We evaluate it experimentally on real datasets and
show that it scales to massive link streams. For example, it allows to obtain a
complete set of communities in under twenty-five minutes for a dataset with
thirty million links, what the state of the art fails to achieve even after a
week of computation. We further show that our method provides communities
similar to DCPM, but slightly more aggregated. We exhibit the relevance of the
obtained communities in real world cases, and show that they provide
information on the importance of vertices in the link streams.Comment: 18 pages, 7 figures, to be published in 30th International Symposium
on Temporal Representation and Reasoning (TIME 2023
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