695 research outputs found
Shared-Memory Parallel Maximal Clique Enumeration
We present shared-memory parallel methods for Maximal Clique Enumeration
(MCE) from a graph. MCE is a fundamental and well-studied graph analytics task,
and is a widely used primitive for identifying dense structures in a graph. Due
to its computationally intensive nature, parallel methods are imperative for
dealing with large graphs. However, surprisingly, there do not yet exist
scalable and parallel methods for MCE on a shared-memory parallel machine. In
this work, we present efficient shared-memory parallel algorithms for MCE, with
the following properties: (1) the parallel algorithms are provably
work-efficient relative to a state-of-the-art sequential algorithm (2) the
algorithms have a provably small parallel depth, showing that they can scale to
a large number of processors, and (3) our implementations on a multicore
machine shows a good speedup and scaling behavior with increasing number of
cores, and are substantially faster than prior shared-memory parallel
algorithms for MCE.Comment: 10 pages, 3 figures, proceedings of the 25th IEEE International
Conference on. High Performance Computing, Data, and Analytics (HiPC), 201
Sublinear-Space Bounded-Delay Enumeration for Massive Network Analytics: Maximal Cliques
Due to the sheer size of real-world networks, delay and space become quite relevant measures for the cost of enumeration in network analytics. This paper presents efficient algorithms for listing maximum cliques in networks, providing the first sublinear-space bounds with guaranteed delay per enumerated clique, thus comparing favorably with the known literature
Searching for network modules
When analyzing complex networks a key target is to uncover their modular
structure, which means searching for a family of modules, namely node subsets
spanning each a subnetwork more densely connected than the average. This work
proposes a novel type of objective function for graph clustering, in the form
of a multilinear polynomial whose coefficients are determined by network
topology. It may be thought of as a potential function, to be maximized, taking
its values on fuzzy clusterings or families of fuzzy subsets of nodes over
which every node distributes a unit membership. When suitably parametrized,
this potential is shown to attain its maximum when every node concentrates its
all unit membership on some module. The output thus is a partition, while the
original discrete optimization problem is turned into a continuous version
allowing to conceive alternative search strategies. The instance of the problem
being a pseudo-Boolean function assigning real-valued cluster scores to node
subsets, modularity maximization is employed to exemplify a so-called quadratic
form, in that the scores of singletons and pairs also fully determine the
scores of larger clusters, while the resulting multilinear polynomial potential
function has degree 2. After considering further quadratic instances, different
from modularity and obtained by interpreting network topology in alternative
manners, a greedy local-search strategy for the continuous framework is
analytically compared with an existing greedy agglomerative procedure for the
discrete case. Overlapping is finally discussed in terms of multiple runs, i.e.
several local searches with different initializations.Comment: 10 page
- …