Model Of Parallel Computation Research Articles

On the Geodetic and Strong Geodetic Parameters of Certain Hypercubic Networks

Networks derived from the hypercube are noted for their efficiency in simulating any bounded-degree communication network and hence they play a significant role in parallel machines. For a graph [Formula: see text], a geodetic cover is a subset [Formula: see text] of [Formula: see text], satisfying the condition that every vertex of [Formula: see text] other than the vertices in [Formula: see text] are covered using geodesics connecting any two vertices in [Formula: see text]. The geodetic number of [Formula: see text] is the least order of such covers in [Formula: see text]. This seminal distance-based parameter is well employed in the areas of location theory, convexity theory and game theory. The strong variant and its edge version are recent variations of the problem that were introduced in due of their applications in social networks. The most established and strong hypercube derivative networks are studied in this paper with respect to certain geodetic parameters. Notably, among the networks that we have considered, the butterfly and the Benes networks belong to the class of bipartite graphs for which the geodetic number problem and its strong version are NP-complete. We have determined the geodetic parameters that include the geodetic number, the strong geodetic number and their corresponding edge variants of the networks taken into consideration. In the process, we have identified a new class of graphs, as semi-extreme edge geodesic graphs and that the enhanced butterfly networks belong to this class. The study of such geodetic parameters in the structural models of parallel computation could be useful for the design of efficient algorithms for the structures considered.

MSI-DTrans: A multi-focus image fusion using multilayer semantic interaction and dynamic transformer

Multi-focus image fusion (MFIF) aims to utilize multiple images with different focal lengths to fuse into a single full-focus image. This process enhances the realism and clarity of the resulting image. In this paper, a MFIF method called MSI-DTrans was proposed. On the one hand, in order to fully utilize all the effective information that the source image carries, the proposed method adopts a multilayer semantic interaction strategy to enhance the interaction of high-frequency and low-frequency information. This approach gradually mines more abstract semantic information, guiding the generation of feature maps from coarse to fine. On the other hand, a parallel multi-scale joint self-attention computation model is designed. The model adopts dynamic sense field and dynamic token embedding to overcome the performance degradation problem when dealing with multi-scale objects. This enables self-attention to integrate long-range dependencies between objects of different scales and reduces computational overhead. Numerous experimental results show that the proposed method effectively avoids image distortion, achieves better visualization results, and demonstrates good competitiveness with many state-of-the-art methods in terms of qualitative and quantitative analysis, as well as efficiency comparison. The source code is available at https://github.com/ouyangbaicai/MSI-DTrans.

Parallel photonic chip for nanosecond end-to-end image processing, transmission, and reconstruction

Image processing, transmission, and reconstruction constitute a major proportion of information technology. The rapid expansion of ubiquitous edge devices and data centers has led to substantial demands on the bandwidth and efficiency of image processing, transmission, and reconstruction. The frequent conversion of serial signals between the optical and electrical domains, coupled with the gradual saturation of electronic processors, has become the bottleneck of end-to-end machine vision. Here, we present an optical parallel computational array chip (OPCA chip) for end-to-end processing, transmission, and reconstruction of optical intensity images. By proposing constructive and destructive computing modes on the large-bandwidth resonant optical channels, a parallel computational model is constructed to implement end-to-end optical neural network computing. The OPCA chip features a measured response time of 6 ns and an optical bandwidth of at least 160 nm. Optical image processing can be efficiently executed with minimal energy consumption and latency, liberated from the need for frequent optical–electronic and analog–digital conversions. The proposed optical computational sensor opens the door to extremely high-speed processing, transmission, and reconstruction of visible contents with nanoseconds response time and terahertz bandwidth.

Explainable graph clustering via expanders in the massively parallel computation model

Explainable clustering provides human-understandable reasons for decisions in black-box learning models. In a previous work, a decision tree built on the set of dimensions was used to define ranges of values for k-means clusters. For explainable graph clustering, we use expander graphs instead of dense subgraphs since powering an expander graph is guaranteed to result in a clique after at most a logarithmic number of steps.Consider a set of multi-dimensional points labeled with k labels. We introduce the heat map sorting problem as reordering the rows and columns of an input matrix (each point is a column and each row is a dimension) such that the labels of the entries of the matrix form connected components (clusters). A cluster is preserved if it remains connected, i.e., if it is not split into several clusters and no two clusters are merged. In the massively parallel computation model (MPC), each machine has a sublinear memory and the total memory of the machines is linear.We prove the problem is NP-hard. We give a fixed-parameter algorithm in MPC and an approximation algorithm based on expander decomposition. We empirically compare our algorithm with explainable k-means on several graphs of email and computer networks.

Multi-scale study on the mechanical properties of concrete based on crack propagation under hygrothermal coupling

During the long-term service of structures, the environmental temperature and humidity fields can lead to the evolution of the pore structure within concrete materials, thereby affecting changes in mechanical properties. However, the mechanisms of their influence still need further clarification and are challenging to correlate for prediction. Addressing this specific issue, the current study focuses on evaluating 78 cubic concrete specimens with C30 and C40 strength grades. These specimens were subjected to a 95 % humidity environment at temperatures of 40 °C, 60 °C, and 80 °C for durations of 30, 60, and 90 days. The research involved conducting both microstructural and macroscopic mechanical tests to quantify the evolution of internal hydrates, pore structures, and pore distribution, as well as to assess the changes in the macroscopic mechanical properties of the specimens. To accurately predict the process, a multiscale finite element model (FEM) based on the bilinear continuum cohesive damage model was established. This model quantifies the changes in mechanical properties of mesoscopic three-phase concrete due to microcrack evolution under hygrothermal coupling. To facilitate multiscale simulations between the Representative Volume Element (RVE) and macroscopic scale models, relevant subroutines were written using Umath, and parallel computing was employed to reduce the computational burden. For the macroscopic model in this study, a homogenized concrete cube model with dimensions identical to the experimental specimens was selected. The effectiveness of the parallel computational model was validated by comparing and analyzing the simulation results under uniaxial compression with the experimental data. The findings indicate that hygrothermal action leads to the initiation and expansion of microcracks within the concrete, thereby impacting the alteration of its mechanical properties. In addition, the parallel computing-based multiscale FEM can more accurately quantify the typical damage process of crack propagation while reducing the computational load and may provide relatively accurate predictions of the mechanical characteristics of concrete under the influence of hygrothermal coupling, ensuring effective modeling of macroscopic structural specimens in various temperature and humidity environments.

Efficient Edge Computing: A Survey of High-Throughput Concurrent Processing Strategies for Graph Data

This paper reviews the strategies for high-throughput concurrent processing of graph data in edge computing environments. As information technology rapidly advances, particularly in areas such as the Internet of Things (IoT), smart cities, and autonomous driving, the need for real-time and efficient data processing continues to grow. Edge computing is a distributed computing paradigm that can process data at or near its origin, thereby reducing network latency, improving application performance, and reducing the load on central data centers. The discussion includes the application of edge computing in graph data processing, highlighting parallel computing models such as the Bulk Synchronous Parallel (BSP) model and other parallel optimization techniques like data partitioning and task scheduling. The paper also addresses specific challenges of parallel processing in edge computing, such as resource constraints, data communication delays, and strategies for security and privacy protection. Despite the significant potential edge computing has demonstrated in processing graph data, numerous challenges remain. Future research directions involve the development of new resource optimization algorithms, low-latency communication protocols, and technologies to enhance data security, aiming to achieve more efficient and secure graph data processing. This paper provides clear directions and a foundation for the efficient implementation of graph data processing in edge computing environments, positioning edge computing to play an increasingly significant role in real-time data analysis and intelligent applications.

Imperative Process Algebra and Models of Parallel Computation

Studies of issues related to computability and computational complexity involve the use of a model of computation. Central in such a model are computational processes. Processes of this kind can be described using an imperative process algebra based on ACP (Algebra of Communicating Processes). In this paper, it is investigated whether the imperative process algebra concerned can play a role in the field of models of computation. It is demonstrated that the process algebra is suitable to describe in a mathematically precise way models of computation corresponding to existing models based on sequential, asynchronous parallel, and synchronous parallel random access machines as well as time and work complexity measures for those models.

Parallel Acyclic Joins: Optimal Algorithms and Cyclicity Separation

We study equi-join computation in the massively parallel computation (MPC) model. Currently, a main open question under this topic is whether it is possible to design an algorithm that can process any join with load O(N polylog N/p 1/ρ* ) — measured in the number of words communicated per machine — where N is the total number of tuples in the input relations, ρ * is the join’s fractional edge covering number, and p is the number of machines. We settle the question in the negative for the class of tuple-based algorithms (all the known MPC join algorithms fall in this class) by proving the existence of a join query with ρ * = 2 that requires a load of Ω ( N/p 1/3 ) to evaluate. Our lower bound provides solid evidence that the “AGM bound” alone is not sufficient for characterizing the hardness of join evaluation in MPC (a phenomenon that does not exist in RAM). The hard join instance identified in our argument is cyclic, which leaves the question of whether O(N polylog N/p 1/ρ* ) is still possible for acyclic joins. We answer this question in the affirmative by showing that any acyclic join can be evaluated with load O(N / p 1/ρ* ), which is asymptotically optimal (there are no polylogarithmic factors in our bound). The separation between cyclic and acyclic joins is yet another phenomenon that is absent in RAM. Our algorithm owes to the discovery of a new mathematical structure — we call “canonical edge cover” — of acyclic hypergraphs, which has numerous non-trivial properties and makes an elegant addition to database theory.

A fresh look at a randomized massively parallel graph coloring algorithm

Petford and Welsh introduced a sequential heuristic algorithm to provide an approximate solution to the NP-hard graph coloring problem. The algorithm is based on the antivoter model and mimics the behavior of a physical process based on a multi-particle system of statistical mechanics. It was later shown that the algorithm can be implemented in a massively parallel model of computation. The increase in computational processing power in recent years allows us to perform an extensive analysis of the algorithms on a larger scale, leading to the possibility of a more comprehensive understanding of the behavior of the algorithm, including the phase transition phenomena.

Inductive definitions in logic versus programs of real-time cellular automata

Descriptive complexity provides intrinsic, i.e. machine-independent, characterizations of the main complexity classes. On the other hand, logic can be useful for designing programs in a natural declarative way. This is especially important for parallel computation models such as cellular automata, since designing parallel programs is considered a difficult task.This paper establishes three logical characterizations of the three classical complexity classes modeling minimal time, called real-time, of one-dimensional cellular automata according to their canonical variations: unidirectional or bidirectional communication, input word given in a parallel or sequential way.Our three logics are natural restrictions of existential second-order Horn logic with built-in successor and predecessor functions. These logics correspond exactly to the three ways of deciding a language on a square grid circuit of side n according to one of the three natural locations of an input word of length n: along a side of the grid, on the diagonal that contains the output cell – placed on the vertex (n,n) of the square grid–, or on the diagonal opposite to the output cell.The key ingredient to our results is a normalization method that transforms a formula from one of our three logics into an equivalent normalized formula that closely mimics a grid circuit.Then, we extend our logics by allowing a limited use of negation on hypotheses like in Stratified Datalog. By revisiting in detail a number of representative classical problems - recognition of the set of primes by Fisher's algorithm, Dyck language recognition, Firing Squad Synchronization problem, etc. - we show that this extension makes easier programming and we prove that it does not change the real-time complexity of our logics.Finally, based on our experience in expressing these representative problems in logic, we argue that our logics are high-level programming languages: they make it possible to express in a natural, complete and synthetic way the algorithms of the literature, based on signals – and even to design new inductive algorithms –, and to translate them automatically into cellular automata of the same complexity.

Computational Parallel on Simulation of Wave Attenuation by Mangrove Forest

Coastal ecosystems, specifically mangrove trees, safeguard coastal regions against natural disasters like erosion, floods, and tsunamis. Numerical simulations employing the Shallow Water Equation (SWE), encompassing mass and momentum conservation equations, are used to comprehend how mangroves attenuate wave energy. The SWE incorporates Manning's friction term, which is directly influenced by mangrove forests. However, the SWE's complexity and sensitivity to initial conditions hinder analytical solutions. Despite its increasing computational demands, we utilize the robust staggered grid method to address this challenge. Our study examines mangroves' wave-attenuating effects and introduces a parallel computational model using OpenMP to expedite computations. Findings reveal that mangroves can reduce wave amplitudes by up to 33% when employing a Manning's coefficient of 0.3 within confined basin simulations. Furthermore, our parallel computing experiments demonstrate substantial computation speed enhancements; the speedup improves up to a point, with a notable 7.26-fold acceleration observed when utilizing eight threads compared to a single line. Moreover, more than a 10-fold acceleration is observed when the number of threads is greater than 16. This underscores the significance of parallelization in exploring mangrove contributions to coastal protection.

Implementation and evaluation of two parallel computational models for the simulation of a long‐haul DWDM system limited by FWM

AbstractFour‐Wave Mixing (FWM) is one of the non‐linear phenomena affecting long‐reach communication systems and high bandwidth. Research communities use simulation tools for parameter optimization. Unfortunately, such a simulation is time‐consuming and requires more time as the number of channels increases. This paper proposes two fast implementations of Dense Wavelength Division Multiplexing (DWDM) system, limited by FWM and the intrinsic Amplified Spontaneous Emission (ASE) noise of optical amplifiers employed in each segment. Additionally, this work compares the efficiency and speed improvement of the proposed parallelization model versus an earlier sequential model. We present the computational complexity analysis of sequential and parallel models. The paper considers two different parallel implementations: a multicore processor using Open MultiProcessing (OpenMP) and Compute Unified Device Architecture (CUDA), which is based on the use of a Graphics Processing Unit (GPU). Results show that parallelism using CUDA improves by up to 70 times the simulation performance compared to the sequential model. Parallelism with CUDA is up to 15 times compared to OpenMP using 12 logical processors. It is possible to simulate an increased number of channels within our parallel execution, which was impractical in the sequential simulation.

Massively parallel and streaming algorithms for balanced clustering

Clustering is a fundamental problem with a wide range of applications. In this paper, we study a balanced version of the well-known k-center clustering problem, where the objective is to select k centers from a given set of points, and assign to each center at most L of the input points, so as to minimize the maximum distance from a point to the center to which it is assigned. We assume soft capacities, where points are allowed to be selected as center more than once. Motivated by applications involving massive datasets, we study the problem in the massively parallel computation (MPC) and streaming models. In particular, we present a two-round MPC algorithm for the balanced k-center problem, achieving an approximation factor of 5α+2, where α is the approximation factor of the corresponding sequential algorithm. This substantially improves the currently best approximation factor of 32α, available for the problem. We show that the approximation factor of our algorithm can be further improved to 5+ε in all spaces with bounded doubling dimension, including the Euclidean space. We also consider the balanced k-center problem in the streaming model, and present a constant-factor streaming algorithm in any metric space using O(knε) memory, and a factor 5+ε streaming algorithm using O(kpolylogn) memory in doubling metrics.

Constrained read-once refutations in UTVPI constraint systems: A parallel perspective

AbstractIn this paper, we analyze two types of refutations for Unit Two Variable Per Inequality (UTVPI) constraints. A UTVPI constraint is a linear inequality of the form: $a_{i}\cdot x_{i}+a_{j} \cdot x_{j} \le b_{k}$ , where $a_{i},a_{j}\in \{0,1,-1\}$ and $b_{k} \in \mathbb{Z}$ . A conjunction of such constraints is called a UTVPI constraint system (UCS) and can be represented in matrix form as: ${\bf A \cdot x \le b}$ . UTVPI constraints are used in many domains including operations research and program verification. We focus on two variants of read-once refutation (ROR). An ROR is a refutation in which each constraint is used at most once. A literal-once refutation (LOR), a more restrictive form of ROR, is a refutation in which each literal ( $x_i$ or $-x_i$ ) is used at most once. First, we examine the constraint-required read-once refutation (CROR) problem and the constraint-required literal-once refutation (CLOR) problem. In both of these problems, we are given a set of constraints that must be used in the refutation. RORs and LORs are incomplete since not every system of linear constraints is guaranteed to have such a refutation. This is still true even when we restrict ourselves to UCSs. In this paper, we provide NC reductions between the CROR and CLOR problems in UCSs and the minimum weight perfect matching problem. The reductions used in this paper assume a CREW PRAM model of parallel computation. As a result, the reductions establish that, from the perspective of parallel algorithms, the CROR and CLOR problems in UCSs are equivalent to matching. In particular, if an NC algorithm exists for either of these problems, then there is an NC algorithm for matching.

A grammatical evolution approach to the automatic inference of P systems

P systems are a bio-inspired framework for defining parallel models of computation. Despite their relevance for both theoretical and application scenarios, the design and the identification of P systems remain tedious and demanding tasks, requiring considerable time and expertise. In this work, we try to address these problems by proposing an automated methodology based on grammatical evolution (GE)—an evolutionary computation technique—which does not require any domain knowledge. We consider a setting where observations of successive configurations of a P system are available, and we rely on GE for automatically inferring the P system, i.e., its ruleset. Such approach directly addresses the identification problem, but it can also be employed for automated design, requiring the designer to simply express the configurations of the P system rather than its full ruleset. We assess the practicability of the proposed method on six problems of various difficulties and evaluate its behavior in terms of inference capability and time consumption. Experimental results confirm our approach is a viable strategy for small problem sizes, where it achieves perfect inference in a few seconds without any human intervention. Moreover, we also obtain promising results for larger problem sizes in a human-aided context, paving the way for fully or partially automated design of P systems.

Design and Simulation of a Hierarchical Parallel Distributed Processing Model for Orientation Selection Based on Primary Visual Cortex.

The study of the human visual system not only helps to understand the mechanism of the visual system but also helps to develop visual aid systems to help the visually impaired. As the systematic study of neural signal processing mechanisms in early biological vision continues, the hierarchical structure of the visual system is gradually being dissected, bringing the possibility of building brain-like computational models from a bionic perspective. In this paper, we follow the objective facts of neurobiology and propose a parallel distributed processing computational model of primary visual cortex orientation selection with reference to the complex process of visual signal processing and transmission between the retina to the primary visual cortex, the hierarchical receptive field structure between cells in each layer, and the very fine-grained parallel distributed characteristics of cortical visual computation, which allow for high speed and efficiency. We approach the design from a brain-like chip perspective, map our network model on the field programmable gate array (FPGA), and perform simulation experiments. The results verify the possibility of implementing our proposed model with programmable devices, which can be applied to small wearable devices with low power consumption and low latency.

Algorithm for Calculation the Carry and Borrow Signs in Multi-digit Operations in the Parallel Computational Model

The fast algorithm to calculate carry signs and borrow signs for implementation of fast multi-digit operations in the parallel computational model is proposed. The proposed algorithm also makes it possible to predict carry signs in the case of an addition operation and predict borrow signs for a subtraction operation. It is shown how the sign prediction algorithm is implemented in operations in which each parallel processor proceeds the separate group of words into which multi-digit numbers are divided. The iterative calculations of carry signs of grouped words are described. The sign calculation algorithm as component of new modifications of multi-digit addition, subtraction, comparison, the sum of three or more numbers in the parallel computational model is presented. The sign calculation algorithm provides general approach to the implementation of multiplication, division, multiplication by modulo, exponentiation by modulo in the parallel computational model. In the form of a table, a general analysis of the complexity of algorithms and an analysis of the complexity by the number of single-word operations per processor are given.

COMPUTATIONAL EXPERIMENTS ON SOLVING GRID ELLIPTIC EQUATIONS BY SOME PARALLEL ITERATIVE METHODS ON THE K60 CLUSTER

The paper deals with the problem of preserving natural water systems, as well as maintaining their integrity, not only through the enterprise of organizational, engineering and technical solutions, but also through the development of highly effective mathematical modeling techniques that make it possible quickly and efficiently, based on interconnected high-precision models of hydrophysics and hydrobiology, predict the processes of pollution spreading and the occurrence of hazardous phenomena in coastal systems. The article considers algorithms for solving grid equations developed for high-performance cluster systems. A model of parallel computations is proposed, which makes it possible, when choosing the appropriate method for solving the problem of aquatic ecology, to estimate the cost of calculations, which is defined as the product of the time of parallel solution of the problem and the number of processors used. An estimate of the optimal amount of information packet for exchange between processors is obtained. The adaptive modified alternating-triangular method of minimum corrections is described, the results of numerical experiments for the parallel variant of this one are presented.

Avoiding the bit-reversed ordering in parallel multi-digit multiplication based on FFT

The paper for the parallel model of computation, a modification of the method of implementing the multiplication of multi-digit integers based on the fast Fourier transform (FFT) avoiding the bit-reversed ordering is proposed. The paper researches the calculation of FFT according to the “butterfly” scheme based on decimation-in- frequency and decimation-in-time methods, an input signal with elements in direct and bit-reversed order, with an increase and decrease in the number Fourier series coefficients at each step of the "butterfly", the use of a list of Fourier series coefficients in direct and bit-reversed order. The standard FFT-based multiplication algorithm uses the same “butterfly” operation to compute the forward and inverse Fourier transforms. The paper analyzes two combinations of the FFTFDN–FFTTBN and FFTFBN–FFTTDN “butterfly” calculation schemes for calculating forward and inverse discrete Fourier transforms (DFT) in the case of implementing the multi-digit operation in parallel computational model to exclude bit-reversed permutation. A scheme for distributing calculations among four processors is proposed, in which forward and inverse Fourier transform calculations are localized within one parallel processor. The proposed modification does not reduce the computational complexity in terms of the number of complex operations, but due to the exclusion of bit-reversed permutation, the number of synchronization commands between processors and data is reduced, which reduces the algorithm execution time. The scheme can be adapted to distribute the computations among a larger number of processors. Four algorithms for implementing FFT based on decimation-in-frequency and decimation-in-time methods, an input vector with elements in direct and bit-reversed orders are presented. To check the result of the calculation, the algorithm of multiplication avoiding the steps of bit-reversed ordering was implemented in the APL programming language. An example of calculation is given in the form of a table.

Pyxel 1.0: an open source Python framework for detector and end-to-end instrument simulation

Detector modeling is becoming more and more critical for the development of new instruments in scientific space missions and ground-based experiments. Modeling tools are often developed from scratch by each individual project and not necessarily shared for reuse by a wider community. To foster knowledge transfer, reusability, and reliability in the instrumentation community, we developed Pyxel, a framework for the simulation of scientific detectors and instruments. Pyxel is an open-source and collaborative project, based on Python, developed as an easy-to-use tool that can host and pipeline any kind of detector effect model. Recently, Pyxel has achieved a new milestone: the public release and launch of version 1.0, which simplified third-party contributions and improved ease of use even further. Since its launch, Pyxel has been experiencing a growing user community and is being used to simulate a variety of detectors. We give a tour of Pyxel’s version 1.0 changes and new features, including a new interface, parallel computing, and new detectors and models. We continue with an example of using Pyxel as a tool for model optimization and calibration. Finally, we describe an example of how Pyxel and its features can be used to develop a full-scale end-to-end instrument simulator.