Sanjukta Bhowmick

Fast Community Detection for Dynamic Complex Networks

Dynamic complex networks are used to model the evolving relationships between entities in widely varying fields of research such as epidemiology, ecology, sociology, and economics. In the study of complex networks, a network is said to have community structure if it divides naturally into groups of vertices with dense connections within groups and sparser connections between groups. Detecting the evolution of communities within dynamically changing networks is crucial to understanding complex systems. In this paper, we develop a fast community detection algorithm for real-time dynamic network data. Our method takes advantage of community information from previous time steps and thereby improves efficiency while maintaining the quality of community detection. Our experiments on citation-based networks show that the execution time improves as much as 30% (average 13%) over static methods.

Adaptive sparse linear solvers for implicit CFD using Newton-Krylov algorithms

We consider the simulation of three-dimensional transonic Euler flow using pseudo-transient Newton-Krylov methods (8,9). The main computation involves solving a large, sparse linear system at each Newton (nonlinear) iteration. We develop a technique for adaptively selecting the linear solver method to match better the numeric properties of the linear systems as they evolve during the course of the nonlinear iterations. We show how such adaptive methods can be implemented using advanced software environments, leading to significant improvements in simulation time. Implicit solution methods play a critical role in compu- tational dynamics (CFD) applications modeled by partial differential equations (PDEs) with different temporal and spatial scales. We consider the solution of the classical problem of three-dimensional transonic Euler about an ONERA M6 wing using pseudo-transient Newton-Krylov methods (8). The majority of computation time in these simulations is spent on solving a large, sparse linear system at each nonlinear iteration, and the numeric properties of these linear systems evolve during the course of the non- linear iterations. In this paper, we develop an approach for adaptively selecting linear solvers to match more closely the evolving numeric properties of the linear systems. We discuss the instantiation of such adaptive methods using advanced software environments, and we report on experi- ments that demonstrate significant improvements in overall simulation time through adaptive methods. Section 2 contains a description of our transonic ap- plication. Section 3 describes the Newton-Krylov algorith- mic framework for the solution of such PDE-based CFD problems and its implementation using advanced software

A Template for Parallelizing the Louvain Method for Modularity Maximization

Detecting communities using modularity maximization is an important operation in network analysis. As the size of the networks increase to petascales, it is important to design parallel algorithms to handle the large-scale data. In this chapter, a shared memory (OpenMP-based) implementation of the Louvain method, one of the most popular algorithms for maximizing modularity, is introduced. This chapter also discusses the challenges in parallelizing this algorithm as well as metrics for evaluating the correctness of the results. The results demonstrate that the implementation is highly scalable. Moreover, it also focuses on how this template can be extended to time-varying networks.

Faster PDE-based simulations using robust composite linear solvers

Many large-scale scientific simulations require the solution of nonlinear partial differential equations (PDEs). The effective solution of such nonlinear PDEs depends to a large extent on efficient and robust sparse linear system solution. In this paper, we show how fast and reliable sparse linear solvers can be composed from several underlying linear solution methods. We present a combinatorial framework for developing optimal composite solvers using metrics such as the execution times and failure rates of base solution schemes. We demonstrate how such composites can be easily instantiated using advanced software environments. Our experiments indicate that overall simulation time can be reduced through highly reliable linear system solution using composite solvers.

Constant Communities in Complex Networks

Identifying community structure is a fundamental problem in network analysis. Most community detection algorithms are based on optimizing a combinatorial parameter, for example modularity. This optimization is generally NP-hard, thus merely changing the vertex order can alter their assignments to the community. However, there has been less study on how vertex ordering influences the results of the community detection algorithms. Here we identify and study the properties of invariant groups of vertices (constant communities) whose assignment to communities are, quite remarkably, not affected by vertex ordering. The percentage of constant communities can vary across different applications and based on empirical results we propose metrics to evaluate these communities. Using constant communities as a pre-processing step, one can significantly reduce the variation of the results. Finally, we present a case study on phoneme network and illustrate that constant communities, quite strikingly, form the core functional units of the larger communities.

Towards high-quality, untangled meshes via a force-directed graph embedding approach

Abstract High quality meshes are crucial for the solution of partial differential equations (PDEs) via the finite element method (or other PDE solvers). The accuracy of the PDE solution, and the stability and conditioning of the stiffness matrix depend upon the mesh quality. In addition, the mesh must be untangled in order for the finite element method to generate physically valid solutions. Tangled meshes, i.e., those with inverted mesh elements, are sometimes generated via large mesh deformations or in the mesh generation process. Traditional techniques for untangling such meshes are based on geometry and/or optimization. Optimization-based mesh untangling techniques first untangle the mesh and then smoothe the resulting untangled mesh in order to obtain high quality meshes; such techniques require the solution of two optimization problems. In this paper, we study how to modify a physical, force-directed method based upon the Fruchterman-Reingold (FR) graph layout algorithm so that it can be used for untangling. The objectives of aesthetic graph layout, such as minimization of edge intersections and near equalization of edge lengths, follow the goals of mesh untangling and generating good quality elements, respectively. Therefore, by using the force-directed method, we can achieve both steps of mesh untangling and mesh smoothing in one operation. We compare the effectiveness of our method with that of the optimization-based mesh untangling method in [1] and implemented in Mesquite by untangling a suite of unstructured triangular, quadrilateral, and tetrahedral finite element volume meshes. The results show that the force-directed method is substantially faster than the Mesquite mesh untangling method without sacrificing much in terms of mesh quality for the majority of the test cases we consider in this paper. The force-directed mesh untangling method demonstrates the most promise on convex geometric domains. Further modifications will be made to the method to improve its ability to untangle meshes on non-convex domains.

A Combinatorial Scheme for Developing Efficient Composite Solvers

Many fundamental problems in scientific computing have more than one solution method. It is not uncommon for alternative solution methods to represent different tradeoffs between solution cost and reliability. Furthermore, the performance of a solution method often depends on the numerical properties of the problem instance and thus can vary dramatically across application domains. In such situations, it is natural to consider the construction of a multi-method composite solver to potentially improve both the average performance and reliability. In this paper, we provide a combinatorial framework for developing such composite solvers. We provide analytical results for obtaining an optimal composite from a set of methods with normalized measures of performance and reliability. Our empirical results demonstrate the effectiveness of such optimal composites for solving large, sparse linear systems of equations.

A Parallel Graph Sampling Algorithm for Analyzing Gene Correlation Networks

Abstract Effcient analysis of complex networks is often a challenging task due to its large size and the noise inherent in the system. One popular method of overcoming this problem is through graph sampling, that is extracting a representative subgraph from the larger network. The accuracy of the sample is validated by comparing the combinatorial properties of the subgraph and the original network. However, there has been little study in comparing networks based on the applications that they represent. Furthermore, sampling methods are generally applied agnostically, without mapping to the requirements of the underlying analysis. In this paper,we introduce a parallel graph sampling algorithm focusing on gene correlation networks. Densely connected subgraphs indicate important functional units of gene products. In our sampling algorithm, we emphasize maintaining highly connected regions of the network through parallel sampling based on extracting the maximal chordal subgraph of the network. We validate our methods by comparing both combinatorial properties and functional units of the subgraphs and larger networks. Our results show that even with significant reduction of the network (on average 20% to 40%), we obtain reliable samplings and many of the relevant combinatorial and functional properties are retained in the subgraphs.

Parallel adaptive solvers in compressible petsc-fun3d simulations

Publisher Summary The chapter presents a polyalgorithmic technique for adaptively selecting the linear solver method to match the numeric properties of linear systems as they evolve during the course of nonlinear iterations. The approach combines more robust but more costly methods when needed in particularly challenging phases of solution, with cheaper, though less powerful, methods in other phases. The chapter demonstrates that this adaptive, polyalgorithmic approach leads to improvements in overall simulation time, is easily parallelized, and is scalable in the context of this large-scale computational fluid dynamics application. This approach reduced overall execution time by using cheaper, though less powerful, linear solvers for relatively easy linear systems and then switching to more robust but more costly methods for more difficult linear systems. The results demonstrate that adaptive solvers can be implemented easily in a multiprocessor environment and are scalable. The chapter investigates adaptive solvers in problem domains and considers more adaptive approaches, including a polynomial heuristic where the trends of the indicators can be estimated by fitting a function to known data points. The chapter also combines adaptive heuristics with high-performance component infrastructure for performance monitoring and analysis.

A noise reducing sampling approach for uncovering critical properties in large scale biological networks

A correlation network is a graph-based representation of relationships among genes or gene products, such as proteins. The advent of high-throughput bioinformatics has resulted in the generation of volumes of data that require sophisticated in silico models, such as the correlation network, for in-depth analysis. Each element in our network represents expression levels of multiple samples of one gene and an edge connecting two nodes reflects the correlation level between the two corresponding genes in the network according to the Pearson correlation coefficient. Biological networks made in this manner are generally found to adhere to a scale-free structural nature, that is, it is modular and adheres to a power-law degree distribution. Filtering these structures to remove noise and coincidental edges in the network is a necessity for network theorists because unfortunately, when examining entire genomes at once, network size and complexity can act as a bottleneck for network manageability. Our previous work demonstrated that chordal graph based sampling of network results in viable models. In this paper, we extend our research to investigate how different orderings affect the results of our sampling, and maintain the viability of resulting network structures. Our results show that chordal graph based sampling not only conserves clusters that are present within the original networks, but by reducing noise can also help uncover additional functional clusters that were previously not obtainable from the original network.