Pub Date : 2020-12-10DOI: 10.1080/23799927.2020.1862302
A. Mesrikhani, M. Farshi, Behnam Iranfar
Developing algorithms that produce approximate solutions is always interesting when we are generating the final solution for a problem. Progressive algorithms report a partial solution to the user which approximates the final solution in some specific steps. Thus, the user can stop the algorithm if the error of the partial solution is tolerable in terms of the application. In this paper, we study the closest pair problem under the Euclidean metric. A progressive algorithm is designed for the closest pair problem, which consists of steps and spends time in each step. In step r, the error of the partial solution is bounded by , where α is the ratio of the maximum pairwise distance and the minimum pairwise distance of points.
{"title":"A progressive algorithm for the closest pair problem","authors":"A. Mesrikhani, M. Farshi, Behnam Iranfar","doi":"10.1080/23799927.2020.1862302","DOIUrl":"https://doi.org/10.1080/23799927.2020.1862302","url":null,"abstract":"Developing algorithms that produce approximate solutions is always interesting when we are generating the final solution for a problem. Progressive algorithms report a partial solution to the user which approximates the final solution in some specific steps. Thus, the user can stop the algorithm if the error of the partial solution is tolerable in terms of the application. In this paper, we study the closest pair problem under the Euclidean metric. A progressive algorithm is designed for the closest pair problem, which consists of steps and spends time in each step. In step r, the error of the partial solution is bounded by , where α is the ratio of the maximum pairwise distance and the minimum pairwise distance of points.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87220446","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 : 2020-12-10DOI: 10.1080/23799927.2020.1861105
Y. Stoyan, G. Yaskov
The problem of packing unequal spheres into a multiconnected domain (container) is considered. Given a set of spheres, the objective is to maximize the packing factor. The problem is considered as a knapsack problem and modelled as a mixed-integer non-linear programming. Characteristics of the model are indicated. We propose a new solution method based on a combination of a branch-and-bound approach and the known local optimization method. The search procedure is represented by a tree which allows handling all possible subsets of spheres. We develop a set of truncation rules to reduce the number of variants under test. The local optimization algorithm proceeds from the assumption of spheres radii being variable. A number of numerical examples are given.
{"title":"Optimized packing unequal spheres into a multiconnected domain: mixed-integer non-linear programming approach","authors":"Y. Stoyan, G. Yaskov","doi":"10.1080/23799927.2020.1861105","DOIUrl":"https://doi.org/10.1080/23799927.2020.1861105","url":null,"abstract":"The problem of packing unequal spheres into a multiconnected domain (container) is considered. Given a set of spheres, the objective is to maximize the packing factor. The problem is considered as a knapsack problem and modelled as a mixed-integer non-linear programming. Characteristics of the model are indicated. We propose a new solution method based on a combination of a branch-and-bound approach and the known local optimization method. The search procedure is represented by a tree which allows handling all possible subsets of spheres. We develop a set of truncation rules to reduce the number of variants under test. The local optimization algorithm proceeds from the assumption of spheres radii being variable. A number of numerical examples are given.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89674493","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 : 2020-12-10DOI: 10.1080/23799927.2020.1859618
F. Safaei, F. K. Jahromi, S. Fathi
ABSTRACT Recursive decomposition of networks is a widely used approach in network analysis for factorization of network structure into small subgraph patterns with few nodes. These patterns are called graphlets (motifs), and their analysis is considered as a common approach in bioinformatics. This paper focuses on evaluating the importance of graphlets in networks and proposes a new analytical model for ranking the graphlets importance based on their contribution to the graph energy spectrum. Besides, a general formula is provided to calculate the graphlet energy contribution to the total energy of a graph; then the energy value of the graph is estimated based on its graphlets. The results of the empirical analysis of synthetic and real networks are consistent with the theoretical results and suggest that the proposed analytical model can accurately estimate the structural features of a given graph based on its graphlets.
{"title":"Graphlets importance ranking in complex networks based on the spectral energy contribution","authors":"F. Safaei, F. K. Jahromi, S. Fathi","doi":"10.1080/23799927.2020.1859618","DOIUrl":"https://doi.org/10.1080/23799927.2020.1859618","url":null,"abstract":"ABSTRACT Recursive decomposition of networks is a widely used approach in network analysis for factorization of network structure into small subgraph patterns with few nodes. These patterns are called graphlets (motifs), and their analysis is considered as a common approach in bioinformatics. This paper focuses on evaluating the importance of graphlets in networks and proposes a new analytical model for ranking the graphlets importance based on their contribution to the graph energy spectrum. Besides, a general formula is provided to calculate the graphlet energy contribution to the total energy of a graph; then the energy value of the graph is estimated based on its graphlets. The results of the empirical analysis of synthetic and real networks are consistent with the theoretical results and suggest that the proposed analytical model can accurately estimate the structural features of a given graph based on its graphlets.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86373850","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 : 2020-12-10DOI: 10.1080/23799927.2020.1854863
Julian Danner, Martin Kreuzer
ABSTRACT For the stream cipher KCipher-2 of the Japanese e-Government Recommended Ciphers List, we present fault attacks requiring only the possibility to reset the cipher and to inject byte faults into certain registers. For the polynomial systems resulting from an injection sequence into one register, we develop a dedicated algebraic solving technique. Using the Marking Algorithm of Horn Logic and the computation of certain Gröbner bases, we optimize the number and locations of fault injection sequences which allow the recovery of the full state of the cipher. The optimal attack requires only about 21 fault injections and 100 seconds for solving the polynomial systems and finding the internal state.
{"title":"A fault attack on KCipher-2","authors":"Julian Danner, Martin Kreuzer","doi":"10.1080/23799927.2020.1854863","DOIUrl":"https://doi.org/10.1080/23799927.2020.1854863","url":null,"abstract":"ABSTRACT For the stream cipher KCipher-2 of the Japanese e-Government Recommended Ciphers List, we present fault attacks requiring only the possibility to reset the cipher and to inject byte faults into certain registers. For the polynomial systems resulting from an injection sequence into one register, we develop a dedicated algebraic solving technique. Using the Marking Algorithm of Horn Logic and the computation of certain Gröbner bases, we optimize the number and locations of fault injection sequences which allow the recovery of the full state of the cipher. The optimal attack requires only about 21 fault injections and 100 seconds for solving the polynomial systems and finding the internal state.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75781280","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 : 2020-12-08DOI: 10.1080/23799927.2020.1861660
A. Rahmani
ABSTRACT Collection and distribution of finished goods through cross-docking to predetermined customers or retailers are practical and challengeable mathematical modelling, optimization, and logistics problems. Thus, appropriate management of the transportation system can help companies decrease their costs and consequently earn more benefits. There is an abundance of modelling proposals in the literature. In this paper, a multi-cross-docking vehicle routing problem (MCVRP) is combined with close–open mixed vehicle routing problem (COMVRP) in the stochastic environment. It is assumed that the fleet of vehicles is heterogeneous. The objective is to minimize the total cost of serving customers. Since the travel time between retailer nodes is non-deterministic, a hybrid solution methodology is developed, which encompasses robust optimization, as well as firefly and genetic algorithm. Computational results demonstrate that the proposed algorithm can efficiently be used to solve the proposed model.
{"title":"A new closed–open vehicle routing approach in stochastic environments","authors":"A. Rahmani","doi":"10.1080/23799927.2020.1861660","DOIUrl":"https://doi.org/10.1080/23799927.2020.1861660","url":null,"abstract":"ABSTRACT Collection and distribution of finished goods through cross-docking to predetermined customers or retailers are practical and challengeable mathematical modelling, optimization, and logistics problems. Thus, appropriate management of the transportation system can help companies decrease their costs and consequently earn more benefits. There is an abundance of modelling proposals in the literature. In this paper, a multi-cross-docking vehicle routing problem (MCVRP) is combined with close–open mixed vehicle routing problem (COMVRP) in the stochastic environment. It is assumed that the fleet of vehicles is heterogeneous. The objective is to minimize the total cost of serving customers. Since the travel time between retailer nodes is non-deterministic, a hybrid solution methodology is developed, which encompasses robust optimization, as well as firefly and genetic algorithm. Computational results demonstrate that the proposed algorithm can efficiently be used to solve the proposed model.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80442093","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 : 2020-12-06DOI: 10.1080/23799927.2020.1860134
K. R. Bhutani, Ravi Kalpathy, H. Mahmoud
We introduce polymer graphs, a class of fast-growing networks endowed with a designated hook. We study the structure of these polymer graphs by investigating numerous average measures such as the average number of nodes of the smallest degree, the average depth of a randomly chosen node, the average degree in the graph, the average order of the sub-polymer graphs hooked into the nodes, the average eccentricity of nodes, and the average diameter of the polymer graph. The construction of polymer graphs presented here relates to the step-growth polymerization.
{"title":"Average measures in polymer graphs","authors":"K. R. Bhutani, Ravi Kalpathy, H. Mahmoud","doi":"10.1080/23799927.2020.1860134","DOIUrl":"https://doi.org/10.1080/23799927.2020.1860134","url":null,"abstract":"We introduce polymer graphs, a class of fast-growing networks endowed with a designated hook. We study the structure of these polymer graphs by investigating numerous average measures such as the average number of nodes of the smallest degree, the average depth of a randomly chosen node, the average degree in the graph, the average order of the sub-polymer graphs hooked into the nodes, the average eccentricity of nodes, and the average diameter of the polymer graph. The construction of polymer graphs presented here relates to the step-growth polymerization.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88674549","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 : 2020-11-28DOI: 10.1080/23799927.2020.1862303
Steve Isaac, Delaram Kahrobaei
We examine two recently proposed public key exchange protocols that are based upon tropical matrix algebras. We observe the first protocol to exhibit a pattern. We introduce a fast attack on the first protocol that exploits this pattern to extract a private parameter of the protocol, and consequently the shared key, in seconds. We go on to show that the second protocol cannot be implemented as it is described in the proposal. The protocol is reliant on an operation being associative. We prove by counterexample that this operation is not associative.
{"title":"A closer look at the tropical cryptography","authors":"Steve Isaac, Delaram Kahrobaei","doi":"10.1080/23799927.2020.1862303","DOIUrl":"https://doi.org/10.1080/23799927.2020.1862303","url":null,"abstract":"We examine two recently proposed public key exchange protocols that are based upon tropical matrix algebras. We observe the first protocol to exhibit a pattern. We introduce a fast attack on the first protocol that exploits this pattern to extract a private parameter of the protocol, and consequently the shared key, in seconds. We go on to show that the second protocol cannot be implemented as it is described in the proposal. The protocol is reliant on an operation being associative. We prove by counterexample that this operation is not associative.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87698866","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 : 2020-11-13DOI: 10.1080/23799927.2020.1850530
M. Grassl
We discuss the connection between quantum error-correcting codes (QECCS) and algebraic coding theory. We start with an introduction to the relevant concepts of quantum mechanics, including the general error model. A quantum error-correcting code is a subspace of a complex Hilbert space, and its error-correcting properties are characterized by the Knill-Laflamme conditions. Using the stabilizer formalism, we illustrate how QECCs for can be constructed using techniques from algebraic coding theory. We also sketch how the information obtained via a quantum measurement can be interpreted as syndrome of the related classical code. Additionally, we present secondary constructions for QECCs, leading to propagation rules for the parameters of QECCs. This includes the puncture code by Rains and construction X for quantum codes.
{"title":"Algebraic quantum codes: linking quantum mechanics and discrete mathematics","authors":"M. Grassl","doi":"10.1080/23799927.2020.1850530","DOIUrl":"https://doi.org/10.1080/23799927.2020.1850530","url":null,"abstract":"We discuss the connection between quantum error-correcting codes (QECCS) and algebraic coding theory. We start with an introduction to the relevant concepts of quantum mechanics, including the general error model. A quantum error-correcting code is a subspace of a complex Hilbert space, and its error-correcting properties are characterized by the Knill-Laflamme conditions. Using the stabilizer formalism, we illustrate how QECCs for can be constructed using techniques from algebraic coding theory. We also sketch how the information obtained via a quantum measurement can be interpreted as syndrome of the related classical code. Additionally, we present secondary constructions for QECCs, leading to propagation rules for the parameters of QECCs. This includes the puncture code by Rains and construction X for quantum codes.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86305552","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 : 2020-11-02DOI: 10.1080/23799927.2020.1831613
Iris Anshel, Derek Atkins, D. Goldfeld, P. Gunnells
ABSTRACT This paper presents an in depth discussion of WalnutDSA, a quantum resistant public-key digital signature method based on the one-way function E-multiplication. A key feature of WalnutDSA is that it provides very efficient means of validating digital signatures which is essential for low-powered and constrained devices. This paper presents an in-depth discussion of the construction of the digital signature algorithm, and delves deeply into the underlying mathematics that facilitates analysing the security of the scheme. When implemented using parameters that defeat all known attacks, WalnutDSA is among the fastest quantum resistant signature verification methods; it performs orders of magnitude faster than ECC, even on low-end embedded hardware. WalnutDSA delivers a 12–25× speed improvement over ECDSA on most platforms, and a 31× speed improvement on a 16-bit microcontroller, making it an ideal solution for low-resource processors found in the Internet of Things (IoT).
{"title":"WalnutDSA™: a group theoretic digital signature algorithm","authors":"Iris Anshel, Derek Atkins, D. Goldfeld, P. Gunnells","doi":"10.1080/23799927.2020.1831613","DOIUrl":"https://doi.org/10.1080/23799927.2020.1831613","url":null,"abstract":"ABSTRACT This paper presents an in depth discussion of WalnutDSA, a quantum resistant public-key digital signature method based on the one-way function E-multiplication. A key feature of WalnutDSA is that it provides very efficient means of validating digital signatures which is essential for low-powered and constrained devices. This paper presents an in-depth discussion of the construction of the digital signature algorithm, and delves deeply into the underlying mathematics that facilitates analysing the security of the scheme. When implemented using parameters that defeat all known attacks, WalnutDSA is among the fastest quantum resistant signature verification methods; it performs orders of magnitude faster than ECC, even on low-end embedded hardware. WalnutDSA delivers a 12–25× speed improvement over ECDSA on most platforms, and a 31× speed improvement on a 16-bit microcontroller, making it an ideal solution for low-resource processors found in the Internet of Things (IoT).","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84319539","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 : 2020-10-01DOI: 10.1080/23799927.2020.1815856
O. Arogundade, S. I. Olotu, O. Abayomi-Alli, S. Misra, A. M. Ikotun
Use case has embedded potentials that enable the diversity in its adoption to addressing other issues in software engineering. This objective of this paper is to gathered and classified use case researches carried out over the years and defines the state-of-art. We identified and analysed 62 relevant articles with deep insights into six different initiatives. The publications included 29 journal articles, 18 conference articles, 3 reports, 5 book chapters, 5 workshops and 2 symposiums. This study deduced that as many as 15 different extensions are proposed from use case ranging from formal descriptions to subjective methodology. Use case has evolved from initial functional requirement elicitation to a more formal and extensive structure. There are fewer publications in cloud computing and use case-based systems. This study contributed to the use case body of knowledge by assessing the extended initiatives and giving an overview of the challenges that are not yet resolved.
{"title":"A study of existing use case extensions and experience: a systematic review","authors":"O. Arogundade, S. I. Olotu, O. Abayomi-Alli, S. Misra, A. M. Ikotun","doi":"10.1080/23799927.2020.1815856","DOIUrl":"https://doi.org/10.1080/23799927.2020.1815856","url":null,"abstract":"Use case has embedded potentials that enable the diversity in its adoption to addressing other issues in software engineering. This objective of this paper is to gathered and classified use case researches carried out over the years and defines the state-of-art. We identified and analysed 62 relevant articles with deep insights into six different initiatives. The publications included 29 journal articles, 18 conference articles, 3 reports, 5 book chapters, 5 workshops and 2 symposiums. This study deduced that as many as 15 different extensions are proposed from use case ranging from formal descriptions to subjective methodology. Use case has evolved from initial functional requirement elicitation to a more formal and extensive structure. There are fewer publications in cloud computing and use case-based systems. This study contributed to the use case body of knowledge by assessing the extended initiatives and giving an overview of the challenges that are not yet resolved.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87132675","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}
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