The K2 stream cipher, designed for 32-bit words, is an ISO/IEC 18033 standard and is listed as a recommended algorithm used by the Japanese government in the CRYPTREC project. The main feature of the K2 algorithm is the use of a dynamic feedback control mechanism between the two linear feedback shift registers, which makes the analysis of the K2 algorithm more difficult. In this paper, for its simplified version algorithm, a key recovery attack is performed by using differential attacks. Firstly, for the unknown key, the same IV is fixed in two chosen IV differential attacks, and we use the input differences and the output differences of the S-box to recover the input of S-box; the internal state values can be uniquely determined by taking intersection of the input of S-box. This technology is used to improve the key recovery attack of seven-round algorithm proposed by Deike Priemuth-Schmid. Secondly, we find the constraint relationship between the keystream equations and the unknown differences by introducing the guess difference bit and eliminate the impossible differences by the constraint relationship. Thus, we expand the key recovery attack from seven to nine rounds. The time complexity of the attack is $boldsymbol{O} boldsymbol{(2^{113.93})}$ , the data complexity is $boldsymbol{O}boldsymbol{(2^{8.71})}$ and the success rate is $textbf{99.07%}$ .
{"title":"Improved Key Recovery Attacks on Simplified Version of K2 Stream Cipher","authors":"Sudong Ma;Jie Guan","doi":"10.1093/comjnl/bxaa154","DOIUrl":"https://doi.org/10.1093/comjnl/bxaa154","url":null,"abstract":"The K2 stream cipher, designed for 32-bit words, is an ISO/IEC 18033 standard and is listed as a recommended algorithm used by the Japanese government in the CRYPTREC project. The main feature of the K2 algorithm is the use of a dynamic feedback control mechanism between the two linear feedback shift registers, which makes the analysis of the K2 algorithm more difficult. In this paper, for its simplified version algorithm, a key recovery attack is performed by using differential attacks. Firstly, for the unknown key, the same IV is fixed in two chosen IV differential attacks, and we use the input differences and the output differences of the S-box to recover the input of S-box; the internal state values can be uniquely determined by taking intersection of the input of S-box. This technology is used to improve the key recovery attack of seven-round algorithm proposed by Deike Priemuth-Schmid. Secondly, we find the constraint relationship between the keystream equations and the unknown differences by introducing the guess difference bit and eliminate the impossible differences by the constraint relationship. Thus, we expand the key recovery attack from seven to nine rounds. The time complexity of the attack is \u0000<tex>$boldsymbol{O} boldsymbol{(2^{113.93})}$</tex>\u0000, the data complexity is \u0000<tex>$boldsymbol{O}boldsymbol{(2^{8.71})}$</tex>\u0000 and the success rate is \u0000<tex>$textbf{99.07%}$</tex>\u0000.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/comjnl/bxaa154","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49941780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce the notion of private set operations (PSO) as a symmetric-key primitive in the cloud scenario, where a client securely outsources his dataset to a cloud service provider and later privately issues queries in the form of common set operations. We define a syntax and security notion for PSO and propose a general construction that satisfies it. There are two main ingredients to our PSO scheme: an adjustable join (Adjoin) scheme (MIT-CSAIL-TR-2012-006 (2012) Cryptographic treatment of CryptDB's adjustable join. http://people.csail.mit.edu/nickolai/papers/popa-join-tr.pdf) and a tuple set (TSet) scheme (Cash, D., Jarecki, S., Jutla, C. S., Krawczyk, H., Rosu, M.-C., and Steiner, M. (2013) Highly-Scalable Searchable Symmetric Encryption With Support for Boolean Queries. 33rd Annual Cryptology Conf., Santa Barbara, CA, August 18–22, pp. 353–373. Springer, Berlin, Heidelberg). We also propose an Adjoin construction that is substantially more efficient (in computation and storage) than the previous ones (Mironov, I., Segev, G., and Shahaf, I. (2017) Strengthening the Security of Encrypted Databases: Non-Transitive Joins. 15th Int. Conf., TCC 2017, Baltimore, MD, USA, November 12–15, pp. 631–661. Springer, Cham) due to the hardness assumption that we rely on, while retaining the same security notion. The proposed PSO scheme can be used to perform join queries on encrypted databases without revealing the duplicate patterns in the unqueried columns, which is inherent to an Adjoin scheme. In addition, we also show that the PSO scheme can be used to perform Boolean search queries on a collection of encrypted documents. We also provide standard security proofs for our constructions and present detailed efficiency evaluation and compare them with well-known previous ones.
{"title":"Private Set Operations Over Encrypted Cloud Dataset and Applications","authors":"Mojtaba Rafiee;Shahram Khazaei","doi":"10.1093/comjnl/bxaa123","DOIUrl":"https://doi.org/10.1093/comjnl/bxaa123","url":null,"abstract":"We introduce the notion of private set operations (PSO) as a symmetric-key primitive in the cloud scenario, where a client securely outsources his dataset to a cloud service provider and later privately issues queries in the form of common set operations. We define a syntax and security notion for PSO and propose a general construction that satisfies it. There are two main ingredients to our PSO scheme: an adjustable join (Adjoin) scheme (MIT-CSAIL-TR-2012-006 (2012) Cryptographic treatment of CryptDB's adjustable join. http://people.csail.mit.edu/nickolai/papers/popa-join-tr.pdf) and a tuple set (TSet) scheme (Cash, D., Jarecki, S., Jutla, C. S., Krawczyk, H., Rosu, M.-C., and Steiner, M. (2013) Highly-Scalable Searchable Symmetric Encryption With Support for Boolean Queries. 33rd Annual Cryptology Conf., Santa Barbara, CA, August 18–22, pp. 353–373. Springer, Berlin, Heidelberg). We also propose an Adjoin construction that is substantially more efficient (in computation and storage) than the previous ones (Mironov, I., Segev, G., and Shahaf, I. (2017) Strengthening the Security of Encrypted Databases: Non-Transitive Joins. 15th Int. Conf., TCC 2017, Baltimore, MD, USA, November 12–15, pp. 631–661. Springer, Cham) due to the hardness assumption that we rely on, while retaining the same security notion. The proposed PSO scheme can be used to perform join queries on encrypted databases without revealing the duplicate patterns in the unqueried columns, which is inherent to an Adjoin scheme. In addition, we also show that the PSO scheme can be used to perform Boolean search queries on a collection of encrypted documents. We also provide standard security proofs for our constructions and present detailed efficiency evaluation and compare them with well-known previous ones.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/comjnl/bxaa123","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49941773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The number of cloud services has dramatically increased over the past few years. Consequently, finding a service with the most suitable quality of service (QoS) criteria matching the user's requirements is becoming a challenging task. Although various decision-making methods have been proposed to help users to find their required cloud services, some uncertainties such as dynamic QoS variations hamper the users from employing such methods. Additionally, the current approaches use either static or average QoS values for cloud service selection and do not consider dynamic QoS variations. In this paper, we overcome this drawback by developing a broker-based approach for cloud service selection. In this approach, we use recently monitored QoS values to find a timeslot weighted satisfaction score that represents how well a service satisfies the user's QoS requirements. The timeslot weighted satisfaction score is then used in Best-Worst Method, which is a multi-criteria decision-making method, to rank the available cloud services. The proposed approach is validated using Amazon's Elastic Compute Cloud (EC2) cloud services performance data. The results show that the proposed approach leads to the selection of more suitable cloud services and is also efficient in terms of performance compared to the existing analytic hierarchy process-based cloud service selection approaches.
{"title":"Dynamic QoS-Aware Cloud Service Selection Using Best-Worst Method and Timeslot Weighted Satisfaction Scores","authors":"Falak Nawaz;Naeem Khalid Janjua","doi":"10.1093/comjnl/bxaa039","DOIUrl":"https://doi.org/10.1093/comjnl/bxaa039","url":null,"abstract":"The number of cloud services has dramatically increased over the past few years. Consequently, finding a service with the most suitable quality of service (QoS) criteria matching the user's requirements is becoming a challenging task. Although various decision-making methods have been proposed to help users to find their required cloud services, some uncertainties such as dynamic QoS variations hamper the users from employing such methods. Additionally, the current approaches use either static or average QoS values for cloud service selection and do not consider dynamic QoS variations. In this paper, we overcome this drawback by developing a broker-based approach for cloud service selection. In this approach, we use recently monitored QoS values to find a timeslot weighted satisfaction score that represents how well a service satisfies the user's QoS requirements. The timeslot weighted satisfaction score is then used in Best-Worst Method, which is a multi-criteria decision-making method, to rank the available cloud services. The proposed approach is validated using Amazon's Elastic Compute Cloud (EC2) cloud services performance data. The results show that the proposed approach leads to the selection of more suitable cloud services and is also efficient in terms of performance compared to the existing analytic hierarchy process-based cloud service selection approaches.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/comjnl/bxaa039","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49951682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Given a graph, the status of a vertex is the sum of the distances between the vertex and all other vertices. The minimum status of a graph is the minimum of statuses of all vertices of this graph. We give a sharp upper bound for the minimum status of a connected graph with fixed order and matching number (domination number, respectively) and characterize the unique trees achieving the bound. We also determine the unique tree such that its minimum status is as small as possible when order and matching number (domination number, respectively) are fixed.
{"title":"Minimum Status, Matching and Domination of Graphs","authors":"Caixia Liang;Bo Zhou;Haiyan Guo","doi":"10.1093/comjnl/bxaa057","DOIUrl":"https://doi.org/10.1093/comjnl/bxaa057","url":null,"abstract":"Given a graph, the status of a vertex is the sum of the distances between the vertex and all other vertices. The minimum status of a graph is the minimum of statuses of all vertices of this graph. We give a sharp upper bound for the minimum status of a connected graph with fixed order and matching number (domination number, respectively) and characterize the unique trees achieving the bound. We also determine the unique tree such that its minimum status is as small as possible when order and matching number (domination number, respectively) are fixed.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/comjnl/bxaa057","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49951685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Algorithmic problem of computing the most influential nodes in an arbitrary graph (influence maximization) is an important theoretical and practical problem and has been extensively studied for decades. For massive graphs (e.g. modelling huge social networks), randomized algorithms are the answer as the exact computation is prohibitively complex, both for runtime and space. This paper concentrates on developing new accurate and efficient randomized algorithms that drastically cut the memory footprint and scale up the computation of the most influential nodes. Implementing the Reverse Influence Sampling method proposed by Borgs, Brautbar, Chayes and Lucier in 2013, we engineered a novel algorithm, CutTheTail (CTT), which solves the problem of influence maximization (IM) while using up to five orders of magnitude smaller space than the existing renown algorithms. CTT is a heuristic algorithm. We tested the accuracy of CTT on large real-world graphs using Monte Carlo simulation as the benchmark and comparing the quality of CTT solution to the algorithms with theoretically proven guaranteed approximation to optimal. Experiments show that CTT provides solutions with the quality equal to the quality of such algorithms. Savings in required space allow to successfully run CTT on a consumer-grade laptop for a graph with almost a billion of edges. To the best of our knowledge, no other IM algorithm can compute a solution on such a scale using a 16 GB RAM laptop.
{"title":"CutTheTail: An Accurate and Space-Efficient Heuristic Algorithm for Influence Maximization","authors":"Diana Popova;Ken-ichi Kawarabayashi;Alex Thomo","doi":"10.1093/comjnl/bxaa049","DOIUrl":"https://doi.org/10.1093/comjnl/bxaa049","url":null,"abstract":"Algorithmic problem of computing the most influential nodes in an arbitrary graph (influence maximization) is an important theoretical and practical problem and has been extensively studied for decades. For massive graphs (e.g. modelling huge social networks), randomized algorithms are the answer as the exact computation is prohibitively complex, both for runtime and space. This paper concentrates on developing new accurate and efficient randomized algorithms that drastically cut the memory footprint and scale up the computation of the most influential nodes. Implementing the Reverse Influence Sampling method proposed by Borgs, Brautbar, Chayes and Lucier in 2013, we engineered a novel algorithm, CutTheTail (CTT), which solves the problem of influence maximization (IM) while using up to five orders of magnitude smaller space than the existing renown algorithms. CTT is a heuristic algorithm. We tested the accuracy of CTT on large real-world graphs using Monte Carlo simulation as the benchmark and comparing the quality of CTT solution to the algorithms with theoretically proven guaranteed approximation to optimal. Experiments show that CTT provides solutions with the quality equal to the quality of such algorithms. Savings in required space allow to successfully run CTT on a consumer-grade laptop for a graph with almost a billion of edges. To the best of our knowledge, no other IM algorithm can compute a solution on such a scale using a 16 GB RAM laptop.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/comjnl/bxaa049","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49951683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem of determining closed-form solutions for some structural parameters of great interest on networked models is meaningful and intriguing. In this paper, we propose a family of networked models $mathcal{G}_{n}(t)$ with hierarchical structure where $t$ represents time step and $n$ is copy number. And then, we study some structural parameters on the proposed models $mathcal{G}_{n}(t)$ in more detail. The results show that (i) models $mathcal{G}_{n}(t)$ follow power-law distribution with exponent $2$ and thus exhibit density feature; (ii) models $mathcal{G}_{n}(t)$ have both higher clustering coefficients and an ultra-small diameter and so display small-world property; and (iii) models $mathcal{G}_{n}(t)$ possess rich mixing structure because Pearson-correlated coefficients undergo phase transitions unseen in previously published networked models. In addition, we also consider trapping problem on networked models $mathcal{G}_{n}(t)$ and then precisely derive a solution for average trapping time $ATT$ . More importantly, the analytic value for $ATT$ can be approximately equal to the theoretical lower bound in the large graph size limit, implying that models $mathcal{G}_{n}(t)$ are capable of having most optimal trapping efficiency. As a result, we also derive exact solution for another significant parameter, Kemeny's constant. Furthermore, we conduct extensive simulations that are in perfect agreement with all the theoretical deductions.
{"title":"Determining Exact Solutions for Structural Parameters on Hierarchical Networks With Density Feature","authors":"Fei Ma;Ping Wang","doi":"10.1093/comjnl/bxaa067","DOIUrl":"https://doi.org/10.1093/comjnl/bxaa067","url":null,"abstract":"The problem of determining closed-form solutions for some structural parameters of great interest on networked models is meaningful and intriguing. In this paper, we propose a family of networked models \u0000<tex>$mathcal{G}_{n}(t)$</tex>\u0000 with hierarchical structure where \u0000<tex>$t$</tex>\u0000 represents time step and \u0000<tex>$n$</tex>\u0000 is copy number. And then, we study some structural parameters on the proposed models \u0000<tex>$mathcal{G}_{n}(t)$</tex>\u0000 in more detail. The results show that (i) models \u0000<tex>$mathcal{G}_{n}(t)$</tex>\u0000 follow power-law distribution with exponent \u0000<tex>$2$</tex>\u0000 and thus exhibit density feature; (ii) models \u0000<tex>$mathcal{G}_{n}(t)$</tex>\u0000 have both higher clustering coefficients and an ultra-small diameter and so display small-world property; and (iii) models \u0000<tex>$mathcal{G}_{n}(t)$</tex>\u0000 possess rich mixing structure because Pearson-correlated coefficients undergo phase transitions unseen in previously published networked models. In addition, we also consider trapping problem on networked models \u0000<tex>$mathcal{G}_{n}(t)$</tex>\u0000 and then precisely derive a solution for average trapping time \u0000<tex>$ATT$</tex>\u0000. More importantly, the analytic value for \u0000<tex>$ATT$</tex>\u0000 can be approximately equal to the theoretical lower bound in the large graph size limit, implying that models \u0000<tex>$mathcal{G}_{n}(t)$</tex>\u0000 are capable of having most optimal trapping efficiency. As a result, we also derive exact solution for another significant parameter, Kemeny's constant. Furthermore, we conduct extensive simulations that are in perfect agreement with all the theoretical deductions.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/comjnl/bxaa067","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49951688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Given a connected graph $G$ and a positive integer $ell $ , the $ell $ -extra (resp. $ell $ -component) edge connectivity of $G$ , denoted by $lambda ^{(ell )}(G)$ (resp. $lambda _{ell }(G)$ ), is the minimum number of edges whose removal from $G$ results in a disconnected graph so that every component has more than $ell $ vertices (resp. so that it contains at least $ell $ components). This naturally generalizes the classical edge connectivity of graphs defined in term of the minimum edge cut. In this paper, we proposed a general approach to derive component (resp. extra) edge connectivity for a connected graph $G$ . For a connected graph $G$ , let $S$ be a vertex subset of $G$ for $Gin {Gamma _{n}(Delta ),AG_n,S_n^2}$ such that $|S|=sleq |V(G)|/2$ , $G[S]$ is connected and $|E(S,G-S)|=min limits _{Usubseteq V(G)}{|E(U, G-U)|: |U|=s, G[U] textrm{is connected} }$ , then we prove that $lambda ^{(s-1)}(G)=|E(S,G-S)|$ and $lambda _{s+1}(G)=|E(S,G-S)|+|E(G[S])|$ for $s=3,4,5$ . By exploring the reliability analysis of $AG_n$ and $S_n^2$ based on extra (component) edge faults, we obtain the following results: (i) $lambda _3(AG_n)-1=lambda ^{(1)}(AG_n)=4n-10$ , $lambda _4(AG_n)-3=lambda ^{(2)}(AG_n)=6n-18$ and $lambda _5(AG_n)-4=lambda ^{(3)}(AG_n)=8n-24$ ; (ii) $lambda _3(S_n^2)-1=lambda ^{(1)}(S_n^2)=4n-8$ , $lambda _4(S_n^2)-3=lambda ^{(2)}(S_n^2)=6n-15$ and $lambda _5(S_n^2)-4=lambda ^{(3)}(S_n^2)=8n-20$ . This general approach maybe applied to many diverse networks.
{"title":"Reliability Analysis of Alternating Group Graphs and Split-Stars","authors":"Mei-Mei Gu;Rong-Xia Hao;Jou-Ming Chang","doi":"10.1093/comjnl/bxaa070","DOIUrl":"https://doi.org/10.1093/comjnl/bxaa070","url":null,"abstract":"Given a connected graph \u0000<tex>$G$</tex>\u0000 and a positive integer \u0000<tex>$ell $</tex>\u0000, the \u0000<tex>$ell $</tex>\u0000-extra (resp. \u0000<tex>$ell $</tex>\u0000-component) edge connectivity of \u0000<tex>$G$</tex>\u0000, denoted by \u0000<tex>$lambda ^{(ell )}(G)$</tex>\u0000 (resp. \u0000<tex>$lambda _{ell }(G)$</tex>\u0000), is the minimum number of edges whose removal from \u0000<tex>$G$</tex>\u0000 results in a disconnected graph so that every component has more than \u0000<tex>$ell $</tex>\u0000 vertices (resp. so that it contains at least \u0000<tex>$ell $</tex>\u0000 components). This naturally generalizes the classical edge connectivity of graphs defined in term of the minimum edge cut. In this paper, we proposed a general approach to derive component (resp. extra) edge connectivity for a connected graph \u0000<tex>$G$</tex>\u0000. For a connected graph \u0000<tex>$G$</tex>\u0000, let \u0000<tex>$S$</tex>\u0000 be a vertex subset of \u0000<tex>$G$</tex>\u0000 for \u0000<tex>$Gin {Gamma _{n}(Delta ),AG_n,S_n^2}$</tex>\u0000 such that \u0000<tex>$|S|=sleq |V(G)|/2$</tex>\u0000, \u0000<tex>$G[S]$</tex>\u0000 is connected and \u0000<tex>$|E(S,G-S)|=min limits _{Usubseteq V(G)}{|E(U, G-U)|: |U|=s, G[U] textrm{is connected} }$</tex>\u0000, then we prove that \u0000<tex>$lambda ^{(s-1)}(G)=|E(S,G-S)|$</tex>\u0000 and \u0000<tex>$lambda _{s+1}(G)=|E(S,G-S)|+|E(G[S])|$</tex>\u0000 for \u0000<tex>$s=3,4,5$</tex>\u0000. By exploring the reliability analysis of \u0000<tex>$AG_n$</tex>\u0000 and \u0000<tex>$S_n^2$</tex>\u0000 based on extra (component) edge faults, we obtain the following results: (i) \u0000<tex>$lambda _3(AG_n)-1=lambda ^{(1)}(AG_n)=4n-10$</tex>\u0000, \u0000<tex>$lambda _4(AG_n)-3=lambda ^{(2)}(AG_n)=6n-18$</tex>\u0000 and \u0000<tex>$lambda _5(AG_n)-4=lambda ^{(3)}(AG_n)=8n-24$</tex>\u0000; (ii) \u0000<tex>$lambda _3(S_n^2)-1=lambda ^{(1)}(S_n^2)=4n-8$</tex>\u0000, \u0000<tex>$lambda _4(S_n^2)-3=lambda ^{(2)}(S_n^2)=6n-15$</tex>\u0000 and \u0000<tex>$lambda _5(S_n^2)-4=lambda ^{(3)}(S_n^2)=8n-20$</tex>\u0000. This general approach maybe applied to many diverse networks.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/comjnl/bxaa070","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49951689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Diagnosability is an important metric to fault tolerance and reliability for multiprocessor systems. However, plenty of research on fault diagnosability focuses on node failure. In practical scenario, not only node failures take place but also link malfunctions may arise. In this work, we investigate the diagnosability of general regular networks with failing nodes as well as missing malfunctional links. Let $S$ be a set of the missing links and broken-down nodes. We first prove that the diagnosability of the survival graph $Gsetminus S$ persists $delta (Gsetminus S)$ under the PMC model (Preparata, F.P., Metze, G. and Chien, R.T. (1967) On the connection assignment problem of diagnosable systems. IEEE Trans. Electron. Comput., EC-16, 848–854) for a $t$ -regular and $t$ -connected triangle-free network $G$ subject to $|S|leq t-1$ and $|V(G)|geq 3t-2$ ( $tgeq 3$ ). Furthermore, we determine the diagnosability of $Gsetminus S$ for some kinds of extensively explored $t$ -regular networks with triangles subject to $|S|leq t-1$ ( $tgeq 3$ ).
{"title":"Persistence of Hybrid Diagnosability of Regular Networks Under Testing Diagnostic Model","authors":"Guanqin Lian;Shuming Zhou;Eddie Cheng;Jiafei Liu;Gaolin Chen","doi":"10.1093/comjnl/bxaa065","DOIUrl":"https://doi.org/10.1093/comjnl/bxaa065","url":null,"abstract":"Diagnosability is an important metric to fault tolerance and reliability for multiprocessor systems. However, plenty of research on fault diagnosability focuses on node failure. In practical scenario, not only node failures take place but also link malfunctions may arise. In this work, we investigate the diagnosability of general regular networks with failing nodes as well as missing malfunctional links. Let \u0000<tex>$S$</tex>\u0000 be a set of the missing links and broken-down nodes. We first prove that the diagnosability of the survival graph \u0000<tex>$Gsetminus S$</tex>\u0000 persists \u0000<tex>$delta (Gsetminus S)$</tex>\u0000 under the PMC model (Preparata, F.P., Metze, G. and Chien, R.T. (1967) On the connection assignment problem of diagnosable systems. IEEE Trans. Electron. Comput., EC-16, 848–854) for a \u0000<tex>$t$</tex>\u0000-regular and \u0000<tex>$t$</tex>\u0000-connected triangle-free network \u0000<tex>$G$</tex>\u0000 subject to \u0000<tex>$|S|leq t-1$</tex>\u0000 and \u0000<tex>$|V(G)|geq 3t-2$</tex>\u0000 (\u0000<tex>$tgeq 3$</tex>\u0000). Furthermore, we determine the diagnosability of \u0000<tex>$Gsetminus S$</tex>\u0000 for some kinds of extensively explored \u0000<tex>$t$</tex>\u0000-regular networks with triangles subject to \u0000<tex>$|S|leq t-1$</tex>\u0000 (\u0000<tex>$tgeq 3$</tex>\u0000).","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/comjnl/bxaa065","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49951687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Most important scientific and engineering applications have complex computations or large data. In all these applications, a huge amount of time is consumed by nested loops. Therefore, loops are the main source of the parallelization of scientific and engineering programs. Many parallelizing compilers focus on parallelization of nested loops with uniform dependences, and parallelization of nested loops with non-uniform dependences has not been extensively investigated. This paper addresses the problem of parallelizing two-level nested loops with non-uniform dependences. The aim is to minimize the execution time by improving the load balancing and minimizing the inter-processor communication. We propose a new tiling algorithm, k-StepIntraTiling, using bin packing problem to minimize the execution time. We demonstrate the effectiveness of the proposed method in several experiments. Simulation and experimental results show that the algorithm effectively reduces the total execution time of several benchmarks compared to the other tiling methods.
{"title":"Intra-Tile Parallelization for Two-Level Perfectly Nested Loops With Non-Uniform Dependences","authors":"Zahra Abdi Reyhan;Shahriar Lotfi;Ayaz Isazadeh;Jaber Karimpour","doi":"10.1093/comjnl/bxaa050","DOIUrl":"https://doi.org/10.1093/comjnl/bxaa050","url":null,"abstract":"Most important scientific and engineering applications have complex computations or large data. In all these applications, a huge amount of time is consumed by nested loops. Therefore, loops are the main source of the parallelization of scientific and engineering programs. Many parallelizing compilers focus on parallelization of nested loops with uniform dependences, and parallelization of nested loops with non-uniform dependences has not been extensively investigated. This paper addresses the problem of parallelizing two-level nested loops with non-uniform dependences. The aim is to minimize the execution time by improving the load balancing and minimizing the inter-processor communication. We propose a new tiling algorithm, k-StepIntraTiling, using bin packing problem to minimize the execution time. We demonstrate the effectiveness of the proposed method in several experiments. Simulation and experimental results show that the algorithm effectively reduces the total execution time of several benchmarks compared to the other tiling methods.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/comjnl/bxaa050","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49951684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As the number of servers in a data center network (DCN) increases, the probability of server failures is significantly increased. Traditional connectivity is an important metric to measure the reliability of DCN. However, the traditional connectivity of a DCN based on the condition of arbitrary faulty servers is generally lower. Therefore, it is important to increase the connectivity of a DCN by adding some limited conditions for the faulty server set. As a result, $g$ -restricted connectivity and $h$ -extra connectivity, which are two crucial subjects for a DCN's ability to tolerate faulty servers, were proposed in the literature. In this paper, we study the $g$ -restricted connectivity and $h$ -extra connectivity of a new server-centric DCN, called BCDC, based on crossed cube with excellent performance. We prove that the $g$ -restricted connectivity of BCDC is 4 for $n=3$ and $2n+g(n-2)-2$ for $ngeq 4$ , where $0leq gleq n-3$ , and the $h$ -extra connectivity of BCDC is 4 for $n=3$ and $2n+h(n-2)-2$ for $ngeq 4$ , where $0leq hleq n-3$ .
{"title":"The Conditional Reliability Evaluation of Data Center Network BCDC","authors":"Mengjie Lv;Baolei Cheng;Jianxi Fan;Xi Wang;Jingya Zhou;Jia Yu","doi":"10.1093/comjnl/bxaa078","DOIUrl":"https://doi.org/10.1093/comjnl/bxaa078","url":null,"abstract":"As the number of servers in a data center network (DCN) increases, the probability of server failures is significantly increased. Traditional connectivity is an important metric to measure the reliability of DCN. However, the traditional connectivity of a DCN based on the condition of arbitrary faulty servers is generally lower. Therefore, it is important to increase the connectivity of a DCN by adding some limited conditions for the faulty server set. As a result, \u0000<tex>$g$</tex>\u0000-restricted connectivity and \u0000<tex>$h$</tex>\u0000-extra connectivity, which are two crucial subjects for a DCN's ability to tolerate faulty servers, were proposed in the literature. In this paper, we study the \u0000<tex>$g$</tex>\u0000-restricted connectivity and \u0000<tex>$h$</tex>\u0000-extra connectivity of a new server-centric DCN, called BCDC, based on crossed cube with excellent performance. We prove that the \u0000<tex>$g$</tex>\u0000-restricted connectivity of BCDC is 4 for \u0000<tex>$n=3$</tex>\u0000 and \u0000<tex>$2n+g(n-2)-2$</tex>\u0000 for \u0000<tex>$ngeq 4$</tex>\u0000, where \u0000<tex>$0leq gleq n-3$</tex>\u0000, and the \u0000<tex>$h$</tex>\u0000-extra connectivity of BCDC is 4 for \u0000<tex>$n=3$</tex>\u0000 and \u0000<tex>$2n+h(n-2)-2$</tex>\u0000 for \u0000<tex>$ngeq 4$</tex>\u0000, where \u0000<tex>$0leq hleq n-3$</tex>\u0000.","PeriodicalId":50641,"journal":{"name":"Computer Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/comjnl/bxaa078","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49951691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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