A Distributed Parallel Random Walk Algorithm for Large-Scale Capacitance Extraction and Simulation

With the advancement of fabrication technology, the electrostatic coupling has increasing impact on the performance of very large-scale integrated (VLSI) circuits and micro-electromechanical systems (MEMS). For the structures in VLSI circuits which are mostly rectilinear geometries, the floating random walk (FRW) method using cubic transition domains has been successfully applied to calculate the electric capacitances among interconnect wires. It is also applicable to the calculation of electric field intensity, which becomes important for nowadays nanometer-technology circuits. In this chapter, an efficient approach is presented to parallelize the FRW algorithm with the graphic processing units (GPUs). GPU-friendly algorithmic flow and data structure are designed to reduce the divergence among random walks and the time of accessing the device memory. The techniques accelerating the extraction of multi-dielectric structures and for extracting multiple nets concurrently are also discussed. Numerical results are presented with several simple structures and larger ones from real VLSI circuits or MEMS. The results validate the accuracy of the presented techniques and demonstrate several tens times speedup due to the GPU-based parallel computing.

Capacitance extraction for interconnect parasitics modeling is the basis of accurate circuit simulation and physical verification for quality integrated circuit (IC) design. Due to its scalability and reliability, the floating random walk (FRW) based solver has been widely used for the capacitance extraction. In this paper, the recently developed techniques on distributed parallel FRW solver and for handling complex floating metals are presented. With them, the efficiency and accuracy of capacitance extraction/simulation for very large-scale integration (VLSI) circuit design are remarkably improved.

This paper presents techniques that use macromodels in order to extend and improve the floating random walk (FRW) method for capacitance extraction. A macromodel is built for each sub-structure for which it is necessary or convenient to hide its geometry details during capacitance extraction. Then, a macromodel-aware random walk scheme connects the Markovchain random walk inside the macromodels and the FRW outside through scalable blank patch regions. This method can be used for instance to extract capacitances for structure with encrypted sub-structures, and extend the FRW method's capability for structure with complex geometry or repeated layout patterns. Numerical results validate the merits of the proposed method with structures including encrypted FinFET layout, complex geometry features, and cyclic layout patterns.

Heuristic algorithms are effective methods for solving complex optimization problems. The optimal algorithm selection for a specific optimization problem is a challenging task. Fitness landscape analysis (FLA) is used to understand the optimization problem's characteristics and help select the optimal algorithm. A random walk algorithm is an essential technique for FLA in continuous search space. However, most currently proposed random walk algorithms suffer from unbalanced sampling points. This article proposes a Lévy flight-based random walk (LRW) algorithm to address this problem. The Lévy flight is used to generate the proposed random walk algorithm's variable step size and direction. Some tests show that the proposed LRW algorithm performs better in the uniformity of sampling points. Besides, the authors analyze the fitness landscape of the CEC2017 benchmark functions using the proposed LRW algorithm. The experimental results indicate that the proposed LRW algorithm can better obtain the structural features of the landscape and has better stability than several other RW algorithms.

The non-Manhattan conductor geometry existing in some capacitance extraction problems brings difficulty to the floating random walk (FRW) method using cubic transition domains. In this chapter, techniques are presented to enhance the FRW method for handling the structures with non-Manhattan conductors. Based on the aligned-box distances and corresponding calculating approaches, the techniques for generating the Gaussian surface and constructing axis-aligned transition cubes are presented. A practical strategy is then presented to judge the domination relationship of non-Manhattan conductor blocks for building the space management structure with candidate list. Finally, the strategy using rotated transition cube and related space management technique are presented to make further acceleration. Experiments on three-dimensional (3-D) interconnect structures including from eight to one thousand non-Manhattan blocks show that the developed method is from 2.9X to 96X faster than a simple extension of the original FRW method. The developed FRW solver is also up to 39X faster than a boundary element method based solver. Additional experiments are carried out to further validate the accuracy and efficiency of the presented techniques, and to demonstrate their suitability for large and multi-dielectric structures.

The Random Walks (RW) algorithm is one of the most efficient and easy-to-use probabilistic segmentation methods. By combining contrast terms with prior terms, it provides accurate segmentations of medical images in a fully automated manner. However, one of the main drawbacks of using the RW algorithm is that its parameters have to be hand-tuned. we propose a novel discriminative learning framework that estimates the parameters using a training dataset. The main challenge we face is that the training samples are not fully supervised. Specifically, they provide a hard segmentation of the images, instead of a probabilistic segmentation. We overcome this challenge by treating the optimal probabilistic segmentation that is compatible with the given hard segmentation as a latent variable. This allows us to employ the latent support vector machine formulation for parameter estimation. We show that our approach significantly outperforms the baseline methods on a challenging dataset consisting of real clinical 3D MRI volumes of skeletal muscles.

Auto-correlated directional swimming can enhance settlement success and connectivity in fish larvae

The segmentation of tumor on PET images is an important step for treatment planning process during the radiotherapy. In this paper, we present an automatic segmentation method on PET images based on the random walks (RW) algorithm. We propose an extension of the random walks framework to integrate a tumor evolution information, which is the predicted tumor region resulting from a model for lung tumor growth and response to radiotherapy. The region of interest (ROI) and labeled seeds are automatically generated. Our approach is compared to the well-known 40% thresholding method, an adaptive thresholding method, a statistical method (FLAB), and a traditional RW algorithm. The good performance of our method has been confirmed on 7 lung tumor patients who are treated with radiotherapy.

In this paper, we introduce a new algorithm for estimating the lower bounds for the star discrepancy of any arbitrary point sets in [ 0 , 1 ] s [0,1]^{s} . Computing the exact star discrepancy is known to be an NP-hard problem, so we have been looking for effective approximation algorithms. The star discrepancy can be thought of as the maximum of a function called the local discrepancy, and we will develop approximation algorithms to maximize this function. Our algorithm is analogous to the random walk algorithm described in one of our previous papers [M. Alsolami and M. Mascagni, A random walk algorithm to estimate a lower bound of the star discrepancy, Monte Carlo Methods Appl. 28 (2022), 4, 341–348.]. We add a statistical technique to the random walk algorithm by implementing the Metropolis algorithm in random walks on each chosen dimension to accept or reject this movement. We call this Metropolis random walk algorithm. In comparison to all previously known techniques, our new algorithm is superior, especially in high dimensions. Also, it can quickly determine the precise value of the star discrepancy in most of our data sets of various sizes and dimensions, or at least the lower bounds of the star discrepancy.

We present a study demonstrating how random walk algorithms can be used for evolutionary image transition. We design different mutation operators based on uniform and biased random walks and study how their combination with a baseline mutation operator can lead to interesting image transition processes in terms of visual effects and artistic features. Using feature-based analysis we investigate the evolutionary image transition behaviour with respect to different features and evaluate the images constructed during the image transition process. Afterwards, we investigate how modifications of our biased random walk approaches can be used for evolutionary image painting. We introduce an evolutionary image painting approach whose underlying biased random walk can be controlled by a parameter influencing the bias of the random walk and thereby creating different artistic painting effects.

Community Detection method based on Random walk and Multi objective Evolutionary algorithm in complex networks

This thesis discusses several random walk and sampling algorithms and analyses the expected cost of using these algorithms to find target nodes in large graphs. The first algorithms discussed are degree biased random walks. A degree biased random walk variant is introduced entitled Self Avoiding Walk Jump (SAWJ). The innovation is in roughly upper bounding the expected unit cost for SAWJ to find a maximum degree node using a discrete time Markov chain model. Second this thesis estimates the expected unit and linear cost to find a target node in Erdos Renyi (ER) graphs under three variants of star sampling, where a random node is selected and it and its neighbors are sampled. These estimates are shown numerically to be accurate on ER and some real-world graphs. Third this thesis looks at questions tangentially related to analyzing graph search algorithms. Counter examples are given showing greedy wiring or rewiring algorithms do not necessarily construct maximally assortative simple graphs and an estimate is given of the expected samples to find a near maximum value in a set of elements with known distribution but unknown parameterization.

Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this article, we focus on the problem of sampling random walks efficiently in a distributed network and its applications. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain random walk samples. All previous algorithms that compute a random walk sample of length ℓ as a subroutine always do so naively, that is, in O (ℓ) rounds. The main contribution of this article is a fast distributed algorithm for performing random walks. We present a sublinear time distributed algorithm for performing random walks whose time complexity is sublinear in the length of the walk. Our algorithm performs a random walk of length ℓ in Õ (√ℓ D ) rounds ( Õ hides polylog n factors where n is the number of nodes in the network) with high probability on an undirected network, where D is the diameter of the network. For small diameter graphs, this is a significant improvement over the naive O (ℓ) bound. Furthermore, our algorithm is optimal within a poly-logarithmic factor as there exists a matching lower bound [Nanongkai et al. 2011]. We further extend our algorithms to efficiently perform k independent random walks in Õ (√ k ℓ D + k ) rounds. We also show that our algorithm can be applied to speedup the more general Metropolis-Hastings sampling. Our random-walk algorithms can be used to speed up distributed algorithms in applications that use random walks as a subroutine. We present two main applications. First, we give a fast distributed algorithm for computing a random spanning tree (RST) in an arbitrary (undirected unweighted) network which runs in Õ (√ mD ) rounds with high probability ( m is the number of edges). Our second application is a fast decentralized algorithm for estimating mixing time and related parameters of the underlying network. Our algorithm is fully decentralized and can serve as a building block in the design of topologically-aware networks.

The development of science and technology encourages the development of robots. Robots are widely used in various fields of human life to facilitate human life. Robot making has developed both in terms of methods and algorithms used in robots. The use of the montecarlo method and the random walks algorithm are widely implemented in robot designs at present. The basic concept of the Montecarlo method in solving differential equations is the probability of a random walk. Based on the approach in the random step process, the Montecarlo method is known for two types of approach that are quite popular, namely the fixed random walk type and the floating random walk type. For this research, the researcher intends to apply the monte carlo method to control the motion of a randon walk based robot. In this research method, the research stages will be described including needs analysis, application of the monte carlo method, making applications to control robots using Arduino.The results of this research, testing using the Montecarlo method, show that the response of the robot is not too slow, the new robot reacts not too far beyond the existing speed change limit. From the above tests, it can be analyzed that the application of the Montecarlo method is more effective and efficient in measuring motion in the robot. Keywords : Montecarlo Method, Robot Control, Randon Walks

In this work, three variant Time Domain Random Walk (TDRW) algorithms were developed for the problem of solute transport in a single fracture-matrix system, where an arbitrary inlet boundary condition can be applied. One approach performs an additional evaluation of integral in terms of injection boundary and the solution to a Dirac delta case. One method makes use of two functions, dependent on specific boundary conditions, to estimate the particle arrival time. The other additionally introduces the concept of solute injection time, resulting from the injection boundary, into the calculation of particle arrival time. To validate the developed variant algorithms, two benchmark cases are considered with respect to a general Dirichlet injection mode and a Robin injection boundary, respectively. The results from three approaches all make a good agreement with those of inverse Laplace transform method. However, the Monte Carlo nature of the TDRW algorithm implies that the accuracy of the computational result is highly dependent on the number of particles applied in the simulation.