Pub Date : 2021-11-16DOI: 10.1142/s0129626421500195
O. Hamdi-Larbi, Ichrak Mehrez, T. Dufaud
Many applications in scientific computing process very large sparse matrices on parallel architectures. The presented work in this paper is a part of a project where our general aim is to develop an auto-tuner system for the selection of the best matrix compression format in the context of high-performance computing. The target smart system can automatically select the best compression format for a given sparse matrix, a numerical method processing this matrix, a parallel programming model and a target architecture. Hence, this paper describes the design and implementation of the proposed concept. We consider a case study consisting of a numerical method reduced to the sparse matrix vector product (SpMV), some compression formats, the data parallel as a programming model and, a distributed multi-core platform as a target architecture. This study allows extracting a set of important novel metrics and parameters which are relative to the considered programming model. Our metrics are used as input to a machine-learning algorithm to predict the best matrix compression format. An experimental study targeting a distributed multi-core platform and processing random and real-world matrices shows that our system can improve in average up to 7% the accuracy of the machine learning.
{"title":"Machine Learning to Design an Auto-tuning System for the Best Compressed Format Detection for Parallel Sparse Computations","authors":"O. Hamdi-Larbi, Ichrak Mehrez, T. Dufaud","doi":"10.1142/s0129626421500195","DOIUrl":"https://doi.org/10.1142/s0129626421500195","url":null,"abstract":"Many applications in scientific computing process very large sparse matrices on parallel architectures. The presented work in this paper is a part of a project where our general aim is to develop an auto-tuner system for the selection of the best matrix compression format in the context of high-performance computing. The target smart system can automatically select the best compression format for a given sparse matrix, a numerical method processing this matrix, a parallel programming model and a target architecture. Hence, this paper describes the design and implementation of the proposed concept. We consider a case study consisting of a numerical method reduced to the sparse matrix vector product (SpMV), some compression formats, the data parallel as a programming model and, a distributed multi-core platform as a target architecture. This study allows extracting a set of important novel metrics and parameters which are relative to the considered programming model. Our metrics are used as input to a machine-learning algorithm to predict the best matrix compression format. An experimental study targeting a distributed multi-core platform and processing random and real-world matrices shows that our system can improve in average up to 7% the accuracy of the machine learning.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124163348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-11DOI: 10.1142/s0129626421500201
O. Michail, P. Spirakis, Michail Theofilatos
We examine the problem of gathering [Formula: see text] agents (or multi-agent rendezvous) in dynamic graphs which may change in every round. We consider a variant of the [Formula: see text]-interval connectivity model [9] in which all instances (snapshots) are always connected spanning subgraphs of an underlying graph, not necessarily a clique. The agents are identical and not equipped with explicit communication capabilities, and are initially arbitrarily positioned on the graph. The problem is for the agents to gather at the same node, not fixed in advance. We first show that the problem becomes impossible to solve if the underlying graph has a cycle. In light of this, we study a relaxed version of this problem, called weak gathering, where the agents are allowed to gather either at the same node, or at two adjacent nodes. Our goal is to characterize the class of 1-interval connected graphs and initial configurations in which the problem is solvable, both with and without homebases. On the negative side we show that when the underlying graph contains a spanning bicyclic subgraph and satisfies an additional connectivity property, weak gathering is unsolvable, thus we concentrate mainly on unicyclic graphs. As we show, in most instances of initial agent configurations, the agents must meet on the cycle. This adds an additional difficulty to the problem, as they need to explore the graph and recognize the nodes that form the cycle. We provide a deterministic algorithm for the solvable cases of this problem that runs in [Formula: see text] number of rounds.
{"title":"Beyond Rings: Gathering in 1-Interval Connected Graphs","authors":"O. Michail, P. Spirakis, Michail Theofilatos","doi":"10.1142/s0129626421500201","DOIUrl":"https://doi.org/10.1142/s0129626421500201","url":null,"abstract":"We examine the problem of gathering [Formula: see text] agents (or multi-agent rendezvous) in dynamic graphs which may change in every round. We consider a variant of the [Formula: see text]-interval connectivity model [9] in which all instances (snapshots) are always connected spanning subgraphs of an underlying graph, not necessarily a clique. The agents are identical and not equipped with explicit communication capabilities, and are initially arbitrarily positioned on the graph. The problem is for the agents to gather at the same node, not fixed in advance. We first show that the problem becomes impossible to solve if the underlying graph has a cycle. In light of this, we study a relaxed version of this problem, called weak gathering, where the agents are allowed to gather either at the same node, or at two adjacent nodes. Our goal is to characterize the class of 1-interval connected graphs and initial configurations in which the problem is solvable, both with and without homebases. On the negative side we show that when the underlying graph contains a spanning bicyclic subgraph and satisfies an additional connectivity property, weak gathering is unsolvable, thus we concentrate mainly on unicyclic graphs. As we show, in most instances of initial agent configurations, the agents must meet on the cycle. This adds an additional difficulty to the problem, as they need to explore the graph and recognize the nodes that form the cycle. We provide a deterministic algorithm for the solvable cases of this problem that runs in [Formula: see text] number of rounds.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132521463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-11DOI: 10.1142/s0129626421500183
Jiafei Liu, Shuming Zhou, E. Cheng, Gaolin Chen, Min Li
Multiprocessor systems are commonly deployed for big data analysis because of evolution in technologies such as cloud computing, IoT, social network and so on. Reliability evaluation is of significant importance for maintenance and improvement of fault tolerance for multiprocessor systems, and system-level diagnosis is a primary strategy to identify the faulty processors in the systems. In this paper, we first determine the [Formula: see text]-good-neighbor connectivity of the [Formula: see text]-dimensional Bicube-based multiprocessor system [Formula: see text], a novel variant of hypercube. Besides, we establish the [Formula: see text]-good-neighbor diagnosability of the Bicube-based multiprocessor system [Formula: see text] under the PMC and MM* models.
{"title":"Reliability Evaluation of Bicube-Based Multiprocessor System under the g-Good-Neighbor Restriction","authors":"Jiafei Liu, Shuming Zhou, E. Cheng, Gaolin Chen, Min Li","doi":"10.1142/s0129626421500183","DOIUrl":"https://doi.org/10.1142/s0129626421500183","url":null,"abstract":"Multiprocessor systems are commonly deployed for big data analysis because of evolution in technologies such as cloud computing, IoT, social network and so on. Reliability evaluation is of significant importance for maintenance and improvement of fault tolerance for multiprocessor systems, and system-level diagnosis is a primary strategy to identify the faulty processors in the systems. In this paper, we first determine the [Formula: see text]-good-neighbor connectivity of the [Formula: see text]-dimensional Bicube-based multiprocessor system [Formula: see text], a novel variant of hypercube. Besides, we establish the [Formula: see text]-good-neighbor diagnosability of the Bicube-based multiprocessor system [Formula: see text] under the PMC and MM* models.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"355 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122997331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-09DOI: 10.1142/s0129626421500225
Guanlei Xu, Xiaogang Xu, Xiaotong Wang
We discuss the problem of filtering out abnormal states from a larger number of quantum states. For this type of problem with [Formula: see text] items to be searched, both the traditional search by enumeration and classical Grover search algorithm have the complexity about [Formula: see text]. In this letter a novel quantum search scheme with exponential speed up is proposed for abnormal states. First, a new comprehensive quantum operator is well-designed to extract the superposition state containing all abnormal states with unknown number [Formula: see text] with complexity [Formula: see text] in probability 1 via well-designed parallel phase comparison. Then, every abnormal state is achieved respectively from [Formula: see text] abnormal states via [Formula: see text] times’ measurement. Finally, a numerical example is given to show the efficiency of the proposed scheme.
我们讨论了从大量量子态中滤除异常态的问题。对于这类搜索项为[Formula: see text]的问题，传统的枚举搜索和经典的Grover搜索算法都具有[Formula: see text]的复杂度。本文提出了一种新的针对异常状态的指数速度量子搜索方案。首先，设计了一种新的综合量子算子，通过设计好的并行相位比较，提取概率为1的包含所有未知数[公式:见文]、复杂度[公式:见文]的异常态的叠加态。然后，通过【公式:见文】次的测量，分别得到【公式:见文】次的异常状态。最后，通过数值算例验证了该方法的有效性。
{"title":"Abnormal Quantum State Search Based on Parallel Phase Comparison","authors":"Guanlei Xu, Xiaogang Xu, Xiaotong Wang","doi":"10.1142/s0129626421500225","DOIUrl":"https://doi.org/10.1142/s0129626421500225","url":null,"abstract":"We discuss the problem of filtering out abnormal states from a larger number of quantum states. For this type of problem with [Formula: see text] items to be searched, both the traditional search by enumeration and classical Grover search algorithm have the complexity about [Formula: see text]. In this letter a novel quantum search scheme with exponential speed up is proposed for abnormal states. First, a new comprehensive quantum operator is well-designed to extract the superposition state containing all abnormal states with unknown number [Formula: see text] with complexity [Formula: see text] in probability 1 via well-designed parallel phase comparison. Then, every abnormal state is achieved respectively from [Formula: see text] abnormal states via [Formula: see text] times’ measurement. Finally, a numerical example is given to show the efficiency of the proposed scheme.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117023457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-20DOI: 10.1142/s0129626421410012
Junying Liu
In order to overcome the problems of low detection accuracy and long detection time of traditional fault detection methods for CNC machine tools, a new fault detection method for CNC machine tools based on wavelet transform is proposed in this paper. In order to improve the effectiveness of running fault detection of CNC machine tools, a wavelet transform method is used to extract the features of the running fault signals of CNC machine tools. According to the feature extraction results, the convolution calculation of the continuous wavelet transform is used to complete the fault detection of CNC machine tool according to the scale result of fault signal. The experimental results show that, compared with traditional fault detection methods, the detection accuracy and efficiency of this method is significantly better: the highest detection accuracy is 97%, and the lowest detection time is only 1.1s.
{"title":"Fault Detection Method of CNC Machine Tool Based on Wavelet Transform","authors":"Junying Liu","doi":"10.1142/s0129626421410012","DOIUrl":"https://doi.org/10.1142/s0129626421410012","url":null,"abstract":"In order to overcome the problems of low detection accuracy and long detection time of traditional fault detection methods for CNC machine tools, a new fault detection method for CNC machine tools based on wavelet transform is proposed in this paper. In order to improve the effectiveness of running fault detection of CNC machine tools, a wavelet transform method is used to extract the features of the running fault signals of CNC machine tools. According to the feature extraction results, the convolution calculation of the continuous wavelet transform is used to complete the fault detection of CNC machine tool according to the scale result of fault signal. The experimental results show that, compared with traditional fault detection methods, the detection accuracy and efficiency of this method is significantly better: the highest detection accuracy is 97%, and the lowest detection time is only 1.1s.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116241319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-19DOI: 10.1142/s0129626421500171
U. Penchalaiah, V. S. Kumar
Digital Signal Processors (DSP) have a ubiquitous presence in almost all civil and military signal processing applications, including mission critical environments like nuclear reactors, process control etc. Arithmetic and Logic units (ALU), being the heart of any digital signal processor, play critical and decisive roles in achieving the required parameter benchmarks and the overall efficiency and robustness of the digital signal processor. State of the art research has shown successful traction with the performance requirements of critical Multiply-Accumulate (MAC) parameters, like reduced power consumption, small electronic real estate footprint and reduction in delay with the associated design complexity. Judicious placement of its building blocks, namely, the truncated multiplier and half-sum carry generation-sum carry generation (HSCG-SCG) adder in the architectural design of ALU and the type of adder and multiplier circuits selected are the core decisions that decide the overall performance of the ALU. To overcome the drawback and to improve the performance further, this work proposes a new architecture for the square root (SQRT) carry select adder (CSLA) using half-sum generation (HSG), half-carry generation (HCG), full-sum generation (FSG) and full-carry generation (FCG) blocks. The proposed design contains N-bit architecture, and comparative results are considered for 8-bit, 16-bit and 32-bit combinations. All the designs are implemented in the Xilinx ISE environment and the results show that better area, power, and delay performance compared to the state of art methods.
{"title":"Design and Implementation of Low Power and Area Efficient Architecture for High Performance ALU","authors":"U. Penchalaiah, V. S. Kumar","doi":"10.1142/s0129626421500171","DOIUrl":"https://doi.org/10.1142/s0129626421500171","url":null,"abstract":"Digital Signal Processors (DSP) have a ubiquitous presence in almost all civil and military signal processing applications, including mission critical environments like nuclear reactors, process control etc. Arithmetic and Logic units (ALU), being the heart of any digital signal processor, play critical and decisive roles in achieving the required parameter benchmarks and the overall efficiency and robustness of the digital signal processor. State of the art research has shown successful traction with the performance requirements of critical Multiply-Accumulate (MAC) parameters, like reduced power consumption, small electronic real estate footprint and reduction in delay with the associated design complexity. Judicious placement of its building blocks, namely, the truncated multiplier and half-sum carry generation-sum carry generation (HSCG-SCG) adder in the architectural design of ALU and the type of adder and multiplier circuits selected are the core decisions that decide the overall performance of the ALU. To overcome the drawback and to improve the performance further, this work proposes a new architecture for the square root (SQRT) carry select adder (CSLA) using half-sum generation (HSG), half-carry generation (HCG), full-sum generation (FSG) and full-carry generation (FCG) blocks. The proposed design contains N-bit architecture, and comparative results are considered for 8-bit, 16-bit and 32-bit combinations. All the designs are implemented in the Xilinx ISE environment and the results show that better area, power, and delay performance compared to the state of art methods.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"2015 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125895329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-24DOI: 10.1142/s0129626421420019
Mahmoud Mansour, Mohamed Aboshady
The recent rapid spread of deadly epidemics have precipitated an urgent need to speed up the development of different treatments, as well as methods of evaluating their efficacy. The first step towards this is the collection of data relating to the cure rate in groups of patients who have had different treatments applied to them. As most of the available data in these cases is random, it is now the role of statisticians to provide efficient statistical tests to assess the treatment methods through the data. This research aims to provide a new statistical test with high efficiency to reach the right decision with accurate results as quickly as possible using parallel computing algorithms through Wolfram Mathematica software.
{"title":"An Efficient Non-Parametric Statistical Test for Assessing Some Treatment Methods of Clinical Data","authors":"Mahmoud Mansour, Mohamed Aboshady","doi":"10.1142/s0129626421420019","DOIUrl":"https://doi.org/10.1142/s0129626421420019","url":null,"abstract":"The recent rapid spread of deadly epidemics have precipitated an urgent need to speed up the development of different treatments, as well as methods of evaluating their efficacy. The first step towards this is the collection of data relating to the cure rate in groups of patients who have had different treatments applied to them. As most of the available data in these cases is random, it is now the role of statisticians to provide efficient statistical tests to assess the treatment methods through the data. This research aims to provide a new statistical test with high efficiency to reach the right decision with accurate results as quickly as possible using parallel computing algorithms through Wolfram Mathematica software.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128043291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-22DOI: 10.1142/s0129626421420020
Giuseppe Agapito, Marianna Milano, M. Cannataro
A new coronavirus, causing a severe acute respiratory syndrome (COVID-19), was started at Wuhan, China, in December 2019. The epidemic has rapidly spread across the world becoming a pandemic that, as of today, has affected more than 70 million people causing over 2 million deaths. To better understand the evolution of spread of the COVID-19 pandemic, we developed PANC (Parallel Network Analysis and Communities Detection), a new parallel preprocessing methodology for network-based analysis and communities detection on Italian COVID-19 data. The goal of the methodology is to analyze set of homogeneous datasets (i.e. COVID-19 data in several regions) using a statistical test to find similar/dissimilar behaviours, mapping such similarity information on a graph and then using community detection algorithm to visualize and analyze the initial dataset. The methodology includes the following steps: (i) a parallel methodology to build similarity matrices that represent similar or dissimilar regions with respect to data; (ii) an effective workload balancing function to improve performance; (iii) the mapping of similarity matrices into networks where nodes represent Italian regions, and edges represent similarity relationships; (iv) the discovering and visualization of communities of regions that show similar behaviour. The methodology is general and can be applied to world-wide data about COVID-19, as well as to all types of data sets in tabular and matrix format. To estimate the scalability with increasing workloads, we analyzed three synthetic COVID-19 datasets with the size of 90.0[Formula: see text]MB, 180.0[Formula: see text]MB, and 360.0[Formula: see text]MB. Experiments was performed on showing the amount of data that can be analyzed in a given amount of time increases almost linearly with the number of computing resources available. Instead, to perform communities detection, we employed the real data set.
{"title":"Parallel Network Analysis and Communities Detection (PANC) Pipeline for the Analysis and Visualization of COVID-19 Data","authors":"Giuseppe Agapito, Marianna Milano, M. Cannataro","doi":"10.1142/s0129626421420020","DOIUrl":"https://doi.org/10.1142/s0129626421420020","url":null,"abstract":"A new coronavirus, causing a severe acute respiratory syndrome (COVID-19), was started at Wuhan, China, in December 2019. The epidemic has rapidly spread across the world becoming a pandemic that, as of today, has affected more than 70 million people causing over 2 million deaths. To better understand the evolution of spread of the COVID-19 pandemic, we developed PANC (Parallel Network Analysis and Communities Detection), a new parallel preprocessing methodology for network-based analysis and communities detection on Italian COVID-19 data. The goal of the methodology is to analyze set of homogeneous datasets (i.e. COVID-19 data in several regions) using a statistical test to find similar/dissimilar behaviours, mapping such similarity information on a graph and then using community detection algorithm to visualize and analyze the initial dataset. The methodology includes the following steps: (i) a parallel methodology to build similarity matrices that represent similar or dissimilar regions with respect to data; (ii) an effective workload balancing function to improve performance; (iii) the mapping of similarity matrices into networks where nodes represent Italian regions, and edges represent similarity relationships; (iv) the discovering and visualization of communities of regions that show similar behaviour. The methodology is general and can be applied to world-wide data about COVID-19, as well as to all types of data sets in tabular and matrix format. To estimate the scalability with increasing workloads, we analyzed three synthetic COVID-19 datasets with the size of 90.0[Formula: see text]MB, 180.0[Formula: see text]MB, and 360.0[Formula: see text]MB. Experiments was performed on showing the amount of data that can be analyzed in a given amount of time increases almost linearly with the number of computing resources available. Instead, to perform communities detection, we employed the real data set.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133715858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-16DOI: 10.1142/s012962642150016x
Liyang Zhai, Liqiong Xu, Shanshan Yin
Reliability evaluation of interconnection networks is of significant importance to the design and maintenance of interconnection networks. The extra connectivity is an important parameter for the reliability evaluation of interconnection networks. Given a graph [Formula: see text] and a positive integer [Formula: see text], the [Formula: see text]-extra connectivity, denoted by [Formula: see text], is the minimum cardinality of a set of vertices in [Formula: see text], if exists, whose deletion disconnects [Formula: see text] and leaves each remaining component with at least [Formula: see text] vertices. In this paper, we show that the 3-extra connectivity of the [Formula: see text]-enhanced hypercube is [Formula: see text] for [Formula: see text] and [Formula: see text]. Some previous results in [IEEE Trans. Comput. 63 (2014) 1594–1600] and [Theor. Comput. Sci. 799 (2019) 22–31] are extended.
互联网络可靠性评估对互联网络的设计和维护具有重要意义。额外连通性是互联网络可靠性评估的一个重要参数。给定一个图[公式:见文]和一个正整数[公式:见文]，[公式:见文]-额外连接，用[公式:见文]表示，是[公式:见文]中一组顶点的最小基数，如果存在，其删除将断开[公式:见文]，并使每个剩余组件至少具有[公式:见文]顶点。在本文中，我们证明了对于[Formula: see text]和[Formula: see text]， [Formula: see text]增强的超立方体的3-extra连通性为[Formula: see text]。一些先前的研究结果发表在[IEEE Trans.]计算，63 (2014)1594-1600 [j]。第一版。Sci. 799(2019) 22-31。
{"title":"On the 3-Extra Connectivity of Enhanced Hypercubes","authors":"Liyang Zhai, Liqiong Xu, Shanshan Yin","doi":"10.1142/s012962642150016x","DOIUrl":"https://doi.org/10.1142/s012962642150016x","url":null,"abstract":"Reliability evaluation of interconnection networks is of significant importance to the design and maintenance of interconnection networks. The extra connectivity is an important parameter for the reliability evaluation of interconnection networks. Given a graph [Formula: see text] and a positive integer [Formula: see text], the [Formula: see text]-extra connectivity, denoted by [Formula: see text], is the minimum cardinality of a set of vertices in [Formula: see text], if exists, whose deletion disconnects [Formula: see text] and leaves each remaining component with at least [Formula: see text] vertices. In this paper, we show that the 3-extra connectivity of the [Formula: see text]-enhanced hypercube is [Formula: see text] for [Formula: see text] and [Formula: see text]. Some previous results in [IEEE Trans. Comput. 63 (2014) 1594–1600] and [Theor. Comput. Sci. 799 (2019) 22–31] are extended.","PeriodicalId":422436,"journal":{"name":"Parallel Process. Lett.","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126615963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-01DOI: 10.1142/S0129626421500079
Pavan Kumar Perepu
Given a mathematical expression in LaTeX or MathML format, retrieval algorithm extracts similar expressions from a database. In our previous work, we have used Longest Common Subsequence (LCS) algorithm to match two expressions of lengths, [Formula: see text] and [Formula: see text], which takes [Formula: see text] time complexity. If there are [Formula: see text] database expressions, total complexity is [Formula: see text], and an increase in [Formula: see text] also increases this complexity. In the present work, we propose to use parallel LCS algorithm in our retrieval process. Parallel LCS has [Formula: see text] time complexity with [Formula: see text] processors and total complexity can be reduced to [Formula: see text]. For our experimentation, OpenMP based implementation has been used on Intel [Formula: see text] processor with 4 cores. However, for smaller expressions, parallel version takes more time as the implementation overhead dominates the algorithmic improvement. As such, we have proposed to use parallel version, selectively, only on larger expressions, in our retrieval algorithm to achieve better performance. We have compared the sequential and parallel versions of our ME retrieval algorithm, and the performance results have been reported on a database of 829 mathematical expressions.
给定LaTeX或MathML格式的数学表达式，检索算法从数据库中提取类似的表达式。在我们之前的工作中，我们使用了LCS算法来匹配两个长度表达式，[Formula: see text]和[Formula: see text]，这需要[Formula: see text]的时间复杂度。如果存在[Formula: see text]数据库表达式，则总复杂度为[Formula: see text]，并且[Formula: see text]的增加也会增加该复杂度。在目前的工作中，我们建议在我们的检索过程中使用并行LCS算法。并行LCS具有[公式:参见文本]处理器的时间复杂度，并且总复杂度可以降低到[公式:参见文本]。在我们的实验中，基于OpenMP的实现已经在Intel 4核处理器上使用。然而，对于较小的表达式，并行版本需要更多的时间，因为实现开销占算法改进的主导地位。因此，我们建议在检索算法中选择性地只对较大的表达式使用并行版本，以获得更好的性能。我们比较了我们的ME检索算法的顺序和并行版本，并在一个包含829个数学表达式的数据库上报告了性能结果。
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