2,652 research outputs found
QuateXelero : an accelerated exact network motif detection algorithm
Finding motifs in biological, social, technological, and other types of networks has become a widespread method to gain more knowledge about these networks’ structure and function. However, this task is very computationally demanding, because it is highly associated with the graph isomorphism which is an NP problem (not known to belong to P or NP-complete subsets yet). Accordingly, this research is endeavoring to decrease the need to call NAUTY isomorphism detection method, which is the most time-consuming step in many existing algorithms. The work provides an extremely fast motif detection algorithm called QuateXelero, which has a Quaternary Tree data structure in the heart. The proposed algorithm is based on the well-known ESU (FANMOD) motif detection algorithm. The results of experiments on some standard model networks approve the overal superiority of the proposed algorithm, namely QuateXelero, compared with two of the fastest existing algorithms, G-Tries and Kavosh. QuateXelero is especially fastest in constructing the central data structure of the algorithm from scratch based on the input network
Subgraph Frequency Distribution Estimation using Graph Neural Networks
Small subgraphs (graphlets) are important features to describe fundamental
units of a large network. The calculation of the subgraph frequency
distributions has a wide application in multiple domains including biology and
engineering. Unfortunately due to the inherent complexity of this task, most of
the existing methods are computationally intensive and inefficient. In this
work, we propose GNNS, a novel representational learning framework that
utilizes graph neural networks to sample subgraphs efficiently for estimating
their frequency distribution. Our framework includes an inference model and a
generative model that learns hierarchical embeddings of nodes, subgraphs, and
graph types. With the learned model and embeddings, subgraphs are sampled in a
highly scalable and parallel way and the frequency distribution estimation is
then performed based on these sampled subgraphs. Eventually, our methods
achieve comparable accuracy and a significant speedup by three orders of
magnitude compared to existing methods.Comment: accepted by KDD 2022 Workshop on Deep Learning on Graph
Design of Passive Analog Electronic Circuits Using Hybrid Modified UMDA algorithm
Hybrid evolutionary passive analog circuits synthesis method based on modified Univariate Marginal Distribution Algorithm (UMDA) and a local search algorithm is proposed in the paper. The modification of the UMDA algorithm which allows to specify the maximum number of the nodes and the maximum number of the components of the synthesized circuit is proposed. The proposed hybrid approach efficiently reduces the number of the objective function evaluations. The modified UMDA algorithm is used for synthesis of the topology and the local search algorithm is used for determination of the parameters of the components of the designed circuit. As an example the proposed method is applied to a problem of synthesis of the fractional capacitor circuit
Beyond Triangles: A Distributed Framework for Estimating 3-profiles of Large Graphs
We study the problem of approximating the -profile of a large graph.
-profiles are generalizations of triangle counts that specify the number of
times a small graph appears as an induced subgraph of a large graph. Our
algorithm uses the novel concept of -profile sparsifiers: sparse graphs that
can be used to approximate the full -profile counts for a given large graph.
Further, we study the problem of estimating local and ego -profiles, two
graph quantities that characterize the local neighborhood of each vertex of a
graph.
Our algorithm is distributed and operates as a vertex program over the
GraphLab PowerGraph framework. We introduce the concept of edge pivoting which
allows us to collect -hop information without maintaining an explicit
-hop neighborhood list at each vertex. This enables the computation of all
the local -profiles in parallel with minimal communication.
We test out implementation in several experiments scaling up to cores
on Amazon EC2. We find that our algorithm can estimate the -profile of a
graph in approximately the same time as triangle counting. For the harder
problem of ego -profiles, we introduce an algorithm that can estimate
profiles of hundreds of thousands of vertices in parallel, in the timescale of
minutes.Comment: To appear in part at KDD'1
- …