52 research outputs found
Evolutionary Centrality and Maximal Cliques in Mobile Social Networks
This paper introduces an evolutionary approach to enhance the process of
finding central nodes in mobile networks. This can provide essential
information and important applications in mobile and social networks. This
evolutionary approach considers the dynamics of the network and takes into
consideration the central nodes from previous time slots. We also study the
applicability of maximal cliques algorithms in mobile social networks and how
it can be used to find the central nodes based on the discovered maximal
cliques. The experimental results are promising and show a significant
enhancement in finding the central nodes
Computing maximal cliques in link streams
A link stream is a collection of triplets 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 , a
-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
. 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
Fine-grained Search Space Classification for Hard Enumeration Variants of Subset Problems
We propose a simple, powerful, and flexible machine learning framework for
(i) reducing the search space of computationally difficult enumeration variants
of subset problems and (ii) augmenting existing state-of-the-art solvers with
informative cues arising from the input distribution. We instantiate our
framework for the problem of listing all maximum cliques in a graph, a central
problem in network analysis, data mining, and computational biology. We
demonstrate the practicality of our approach on real-world networks with
millions of vertices and edges by not only retaining all optimal solutions, but
also aggressively pruning the input instance size resulting in several fold
speedups of state-of-the-art algorithms. Finally, we explore the limits of
scalability and robustness of our proposed framework, suggesting that
supervised learning is viable for tackling NP-hard problems in practice.Comment: AAAI 201
Border bases for lattice ideals
The main ingredient to construct an O-border basis of an ideal I
K[x1,. .., xn] is the order ideal O, which is a basis of the K-vector space
K[x1,. .., xn]/I. In this paper we give a procedure to find all the possible
order ideals associated with a lattice ideal IM (where M is a lattice of Z n).
The construction can be applied to ideals of any dimension (not only
zero-dimensional) and shows that the possible order ideals are always in a
finite number. For lattice ideals of positive dimension we also show that,
although a border basis is infinite, it can be defined in finite terms.
Furthermore we give an example which proves that not all border bases of a
lattice ideal come from Gr\"obner bases. Finally, we give a complete and
explicit description of all the border bases for ideals IM in case M is a
2-dimensional lattice contained in Z 2 .Comment: 25 pages, 3 figures. Comments welcome!, MEGA'2015 (Special Issue),
Jun 2015, Trento, Ital
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
An Output Sensitive Algorithm for Maximal Clique Enumeration in Sparse Graphs
The degeneracy of a graph G is the smallest integer k such that every subgraph of G contains a vertex of degree at most k. Given an n-order k-degenerate graph G, we present an algorithm for enumerating all its maximal cliques. Assuming that c is the number of maximal cliques of G, our algorithm has setup time O(n(k^2+s(k+1))) and enumeration time cO((k+1)f(k+1)) where s(k+1) (resp. f(k+1)) is the preprocessing time (resp. enumeration time) for maximal clique enumeration in a general (k+1)-order graph. This is the first output sensitive algorithm whose enumeration time depends only on the degeneracy of the graph
DeCAF—Discrimination, Comparison, Alignment Tool for 2D PHarmacophores
Comparison of small molecules is a common component of many cheminformatics workflows, including the design of new compounds and libraries as well as side-effect predictions and drug repurposing. Currently, large-scale comparison methods rely mostly on simple fingerprint representation of molecules, which take into account the structural similarities of compounds. Methods that utilize 3D information depend on multiple conformer generation steps, which are computationally expensive and can greatly influence their results. The aim of this study was to augment molecule representation with spatial and physicochemical properties while simultaneously avoiding conformer generation. To achieve this goal, we describe a molecule as an undirected graph in which the nodes correspond to atoms with pharmacophoric properties and the edges of the graph represent the distances between features. This approach combines the benefits of a conformation-free representation of a molecule with additional spatial information. We implemented our approach as an open-source Python module called DeCAF (Discrimination, Comparison, Alignment tool for 2D PHarmacophores), freely available at http://bitbucket.org/marta-sd/decaf. We show DeCAF’s strengths and weaknesses with usage examples and thorough statistical evaluation. Additionally, we show that our method can be manually tweaked to further improve the results for specific tasks. The full dataset on which DeCAF was evaluated and all scripts used to calculate and analyze the results are also provided
Context-aware Dynamic Data-driven Pattern Classification
AbstractThis work aims to mathematically formalize the notion of context, with the purpose of allowing contextual decision-making in order to improve performance in dynamic data driven classification systems. We present definitions for both intrinsic context, i.e. factors which directly affect sensor measurements for a given event, as well as extrinsic context, i.e. factors which do not affect the sensor measurements directly, but do affect the interpretation of collected data. Supervised and unsupervised modeling techniques to derive context and context labels from sensor data are formulated. Here, supervised modeling incorporates the a priori known factors affecting the sensing modalities, while unsupervised modeling autonomously discovers the structure of those factors in sensor data. Context-aware event classification algorithms are developed by adapting the classification boundaries, dependent on the current operational context. Improvements in context-aware classification have been quantified and validated in an unattended sensor-fence application for US Border Monitoring. Field data, collected with seismic sensors on different ground types, are analyzed in order to classify two types of walking across the border, namely, normal and stealthy. The classification is shown to be strongly dependent on the context (specifically, soil type: gravel or moist soil)
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
Listing all maximal cliques in sparse graphs in near-optimal time
The degeneracy of an -vertex graph is the smallest number such that every subgraph of contains a vertex of degree at most . We show that there exists a nearly-optimal fixed-parameter tractable algorithm for enumerating all maximal cliques, parametrized by degeneracy. To achieve this result, we modify the classic Bron--Kerbosch algorithm and show that it runs in time . We also provide matching upper and lower bounds showing that the largest possible number of maximal cliques in an -vertex graph with degeneracy (when is a multiple of 3 and ) is . Therefore, our algorithm matches the worst-case output size of the problem whenever
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