731 research outputs found
Mining Maximal Cliques from an Uncertain Graph
We consider mining dense substructures (maximal cliques) from an uncertain
graph, which is a probability distribution on a set of deterministic graphs.
For parameter 0 < {\alpha} < 1, we present a precise definition of an
{\alpha}-maximal clique in an uncertain graph. We present matching upper and
lower bounds on the number of {\alpha}-maximal cliques possible within an
uncertain graph. We present an algorithm to enumerate {\alpha}-maximal cliques
in an uncertain graph whose worst-case runtime is near-optimal, and an
experimental evaluation showing the practical utility of the algorithm.Comment: ICDE 201
Incremental Maintenance of Maximal Cliques in a Dynamic Graph
We consider the maintenance of the set of all maximal cliques in a dynamic
graph that is changing through the addition or deletion of edges. We present
nearly tight bounds on the magnitude of change in the set of maximal cliques,
as well as the first change-sensitive algorithms for clique maintenance, whose
runtime is proportional to the magnitude of the change in the set of maximal
cliques. We present experimental results showing these algorithms are efficient
in practice and are faster than prior work by two to three orders of magnitude.Comment: 18 pages, 8 figure
Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications
Multilayer networks are a powerful paradigm to model complex systems, where
multiple relations occur between the same entities. Despite the keen interest
in a variety of tasks, algorithms, and analyses in this type of network, the
problem of extracting dense subgraphs has remained largely unexplored so far.
In this work we study the problem of core decomposition of a multilayer
network. The multilayer context is much challenging as no total order exists
among multilayer cores; rather, they form a lattice whose size is exponential
in the number of layers. In this setting we devise three algorithms which
differ in the way they visit the core lattice and in their pruning techniques.
We then move a step forward and study the problem of extracting the
inner-most (also known as maximal) cores, i.e., the cores that are not
dominated by any other core in terms of their core index in all the layers.
Inner-most cores are typically orders of magnitude less than all the cores.
Motivated by this, we devise an algorithm that effectively exploits the
maximality property and extracts inner-most cores directly, without first
computing a complete decomposition.
Finally, we showcase the multilayer core-decomposition tool in a variety of
scenarios and problems. We start by considering the problem of densest-subgraph
extraction in multilayer networks. We introduce a definition of multilayer
densest subgraph that trades-off between high density and number of layers in
which the high density holds, and exploit multilayer core decomposition to
approximate this problem with quality guarantees. As further applications, we
show how to utilize multilayer core decomposition to speed-up the extraction of
frequent cross-graph quasi-cliques and to generalize the community-search
problem to the multilayer setting
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