Generating realistic scaled complex networks

Research on generative models is a central project in the emerging field of network science, and it studies how statistical patterns found in real networks could be generated by formal rules. Output from these generative models is then the basis for designing and evaluating computational methods on networks, and for verification and simulation studies. During the last two decades, a variety of models has been proposed with an ultimate goal of achieving comprehensive realism for the generated networks. In this study, we (a) introduce a new generator, termed ReCoN; (b) explore how ReCoN and some existing models can be fitted to an original network to produce a structurally similar replica, (c) use ReCoN to produce networks much larger than the original exemplar, and finally (d) discuss open problems and promising research directions. In a comparative experimental study, we find that ReCoN is often superior to many other state-of-the-art network generation methods. We argue that ReCoN is a scalable and effective tool for modeling a given network while preserving important properties at both micro- and macroscopic scales, and for scaling the exemplar data by orders of magnitude in size.Comment: 26 pages, 13 figures, extended version, a preliminary version of the paper was presented at the 5th International Workshop on Complex Networks and their Application

Space-Efficient Graph Coarsening with Applications to Succinct Planar Encodings

We present a novel space-efficient graph coarsening technique for n-vertex planar graphs G, called cloud partition, which partitions the vertices V(G) into disjoint sets C of size O(log n) such that each C induces a connected subgraph of G. Using this partition ? we construct a so-called structure-maintaining minor F of G via specific contractions within the disjoint sets such that F has O(n/log n) vertices. The combination of (F, ?) is referred to as a cloud decomposition. For planar graphs we show that a cloud decomposition can be constructed in O(n) time and using O(n) bits. Given a cloud decomposition (F, ?) constructed for a planar graph G we are able to find a balanced separator of G in O(n/log n) time. Contrary to related publications, we do not make use of an embedding of the planar input graph. We generalize our cloud decomposition from planar graphs to H-minor-free graphs for any fixed graph H. This allows us to construct the succinct encoding scheme for H-minor-free graphs due to Blelloch and Farzan (CPM 2010) in O(n) time and O(n) bits improving both runtime and space by a factor of ?(log n). As an additional application of our cloud decomposition we show that, for H-minor-free graphs, a tree decomposition of width O(n^{1/2 + ?}) for any ? > 0 can be constructed in O(n) bits and a time linear in the size of the tree decomposition. A similar result by Izumi and Otachi (ICALP 2020) constructs a tree decomposition of width O(k ?n log n) for graphs of treewidth k ? ?n in sublinear space and polynomial time

Strategic Optimization Techniques For FRTU Deployment and Chip Physical Design

Combinatorial optimization is a complex engineering subject. Although formulation often depends on the nature of problems that differs from their setup, design, constraints, and implications, establishing a unifying framework is essential. This dissertation investigates the unique features of three important optimization problems that can span from small-scale design automation to large-scale power system planning: (1) Feeder remote terminal unit (FRTU) planning strategy by considering the cybersecurity of secondary distribution network in electrical distribution grid, (2) physical-level synthesis for microfluidic lab-on-a-chip, and (3) discrete gate sizing in very-large-scale integration (VLSI) circuit. First, an optimization technique by cross entropy is proposed to handle FRTU deployment in primary network considering cybersecurity of secondary distribution network. While it is constrained by monetary budget on the number of deployed FRTUs, the proposed algorithm identi?es pivotal locations of a distribution feeder to install the FRTUs in different time horizons. Then, multi-scale optimization techniques are proposed for digital micro?uidic lab-on-a-chip physical level synthesis. The proposed techniques handle the variation-aware lab-on-a-chip placement and routing co-design while satisfying all constraints, and considering contamination and defect. Last, the first fully polynomial time approximation scheme (FPTAS) is proposed for the delay driven discrete gate sizing problem, which explores the theoretical view since the existing works are heuristics with no performance guarantee. The intellectual contribution of the proposed methods establishes a novel paradigm bridging the gaps between professional communities

A Comprehensive Survey on Graph Summarization with Graph Neural Networks

As large-scale graphs become more widespread, more and more computational challenges with extracting, processing, and interpreting large graph data are being exposed. It is therefore natural to search for ways to summarize these expansive graphs while preserving their key characteristics. In the past, most graph summarization techniques sought to capture the most important part of a graph statistically. However, today, the high dimensionality and complexity of modern graph data are making deep learning techniques more popular. Hence, this paper presents a comprehensive survey of progress in deep learning summarization techniques that rely on graph neural networks (GNNs). Our investigation includes a review of the current state-of-the-art approaches, including recurrent GNNs, convolutional GNNs, graph autoencoders, and graph attention networks. A new burgeoning line of research is also discussed where graph reinforcement learning is being used to evaluate and improve the quality of graph summaries. Additionally, the survey provides details of benchmark datasets, evaluation metrics, and open-source tools that are often employed in experimentation settings, along with a discussion on the practical uses of graph summarization in different fields. Finally, the survey concludes with a number of open research challenges to motivate further study in this area.Comment: 20 pages, 4 figures, 3 tables, Journal of IEEE Transactions on Artificial Intelligenc

Fast Machine Learning Algorithms for Massive Datasets with Applications in the Biomedical Domain

The continuous increase in the size of datasets introduces computational challenges for machine learning algorithms. In this dissertation, we cover the machine learning algorithms and applications in large-scale data analysis in manufacturing and healthcare. We begin with introducing a multilevel framework to scale the support vector machine (SVM), a popular supervised learning algorithm with a few tunable hyperparameters and highly accurate prediction. The computational complexity of nonlinear SVM is prohibitive on large-scale datasets compared to the linear SVM, which is more scalable for massive datasets. The nonlinear SVM has shown to produce significantly higher classification quality on complex and highly imbalanced datasets. However, a higher classification quality requires a computationally expensive quadratic programming solver and extra kernel parameters for model selection. We introduce a generalized fast multilevel framework for regular, weighted, and instance weighted SVM that achieves similar or better classification quality compared to the state-of-the-art SVM libraries such as LIBSVM. Our framework improves the runtime more than two orders of magnitude for some of the well-known benchmark datasets. We cover multiple versions of our proposed framework and its implementation in detail. The framework is implemented using PETSc library which allows easy integration with scientific computing tasks. Next, we propose an adaptive multilevel learning framework for SVM to reduce the variance between prediction qualities across the levels, improve the overall prediction accuracy, and boost the runtime. We implement multi-threaded support to speed up the parameter fitting runtime that results in more than an order of magnitude speed-up. We design an early stopping criteria to reduce the extra computational cost when we achieve expected prediction quality. This approach provides significant speed-up, especially for massive datasets. Finally, we propose an efficient low dimensional feature extraction over massive knowledge networks. Knowledge networks are becoming more popular in the biomedical domain for knowledge representation. Each layer in knowledge networks can store the information from one or multiple sources of data. The relationships between concepts or between layers represent valuable information. The proposed feature engineering approach provides an efficient and highly accurate prediction of the relationship between biomedical concepts on massive datasets. Our proposed approach utilizes semantics and probabilities to reduce the potential search space for the exploration and learning of machine learning algorithms. The calculation of probabilities is highly scalable with the size of the knowledge network. The number of features is fixed and equivalent to the number of relationships or classes in the data. A comprehensive comparison of well-known classifiers such as random forest, SVM, and deep learning over various features extracted from the same dataset, provides an overview for performance and computational trade-offs. Our source code, documentation and parameters will be available at https://github.com/esadr/

Generating realistic scaled complex networks

Research on generative models plays a central role in the emerging field of network science, studying how statistical patterns found in real networks could be generated by formal rules. Output from these generative models is then the basis for designing and evaluating computational methods on networks including verification and simulation studies. During the last two decades, a variety of models has been proposed with an ultimate goal of achieving comprehensive realism for the generated networks. In this study, we (a) introduce a new generator, termed ReCoN; (b) explore how ReCoN and some existing models can be fitted to an original network to produce a structurally similar replica, (c) use ReCoN to produce networks much larger than the original exemplar, and finally (d) discuss open problems and promising research directions. In a comparative experimental study, we find that ReCoN is often superior to many other state-of-the-art network generation methods. We argue that ReCoN is a scalable and effective tool for modeling a given network while preserving important properties at both micro- and macroscopic scales, and for scaling the exemplar data by orders of magnitude in size

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie