Pub Date : 2020-06-02DOI: 10.1080/23799927.2020.1853238
Mariya Bessonov, D. Grigoriev, V. Shpilrain
In this short note, we address a common misconception at the interface of probability theory and public-key cryptography.
在这篇简短的文章中，我们解决了概率论和公钥密码学之间的一个常见误解。
{"title":"Probability theory and public-key cryptography","authors":"Mariya Bessonov, D. Grigoriev, V. Shpilrain","doi":"10.1080/23799927.2020.1853238","DOIUrl":"https://doi.org/10.1080/23799927.2020.1853238","url":null,"abstract":"In this short note, we address a common misconception at the interface of probability theory and public-key cryptography.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"1 1","pages":"285 - 290"},"PeriodicalIF":0.8,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74350073","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 : 2020-04-05DOI: 10.1080/23799927.2023.2166873
Mohammad Reza Zarrabi, N. M. Charkari
ABSTRACT The purpose of this paper is to give a simple proof for a necessary and sufficient condition for visibility paths in simple polygons. A visibility path is a curve such that every point inside a simple polygon is visible from at least one point on the path. This result is essential for finding the shortest watchman route inside a simple polygon specially when the route is restricted to curved paths.
{"title":"A sufficient condition for visibility paths in simple polygons","authors":"Mohammad Reza Zarrabi, N. M. Charkari","doi":"10.1080/23799927.2023.2166873","DOIUrl":"https://doi.org/10.1080/23799927.2023.2166873","url":null,"abstract":"ABSTRACT The purpose of this paper is to give a simple proof for a necessary and sufficient condition for visibility paths in simple polygons. A visibility path is a curve such that every point inside a simple polygon is visible from at least one point on the path. This result is essential for finding the shortest watchman route inside a simple polygon specially when the route is restricted to curved paths.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"2 1","pages":"93 - 98"},"PeriodicalIF":0.8,"publicationDate":"2020-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91240248","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 : 2020-04-02DOI: 10.1080/23799927.2020.1748115
Wu-Lin Chen, Kuo-Hsiung Wang
This study aims at proposing system reliability and sensitivity analysis of a retrial machine repair problem with warm standbys and imperfect coverage. When an operating or warm standby machine fails, it may be immediately detected, located, and replaced with a coverage probability by a standby if one is available. The Laplace transform technique is adopted to derive two system performance measures, system reliability and mean time to system failure (MTTF). Sensitivity analysis and relative sensitivity are then executed. In order to realize how each system parameter affects performance measures, extensive numerical experiments are designed and the important results are outlined. The results of this study provide a valuable reference for the good design of related real world systems.
{"title":"Reliability and sensitivity analysis of a retrial machine repair problem with warm standbys and imperfect coverage","authors":"Wu-Lin Chen, Kuo-Hsiung Wang","doi":"10.1080/23799927.2020.1748115","DOIUrl":"https://doi.org/10.1080/23799927.2020.1748115","url":null,"abstract":"This study aims at proposing system reliability and sensitivity analysis of a retrial machine repair problem with warm standbys and imperfect coverage. When an operating or warm standby machine fails, it may be immediately detected, located, and replaced with a coverage probability by a standby if one is available. The Laplace transform technique is adopted to derive two system performance measures, system reliability and mean time to system failure (MTTF). Sensitivity analysis and relative sensitivity are then executed. In order to realize how each system parameter affects performance measures, extensive numerical experiments are designed and the important results are outlined. The results of this study provide a valuable reference for the good design of related real world systems.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"7 1","pages":"72 - 86"},"PeriodicalIF":0.8,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81724400","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 : 2020-04-02DOI: 10.1080/23799927.2020.1764626
E. Cheng, K. Qiu, Z. Shen
Diagnosability of a self-diagnosable interconnection structure specifies the maximum number of faulty vertices such a structure can identify by itself. A variety of diagnosability models have been suggested. It turns out that a diagnosability property of a network structure is closely associated with its relevant connectivity property. Based on this observation, a general diagnosability derivation process has been suggested. The g-extra connectivity of a graph G characterizes the size of a minimum vertex set F such that, when it is removed, every component in the disconnected survival graph, contains at least g + 1 vertices. In this paper, we discuss the aforementioned general derivation process, derive the g-extra connectivity, and then apply the aforementioned general process to reveal the g-extra diagnosability of the generalized exchanged hypercube.
{"title":"The g-extra diagnosability of the generalized exchanged hypercube","authors":"E. Cheng, K. Qiu, Z. Shen","doi":"10.1080/23799927.2020.1764626","DOIUrl":"https://doi.org/10.1080/23799927.2020.1764626","url":null,"abstract":"Diagnosability of a self-diagnosable interconnection structure specifies the maximum number of faulty vertices such a structure can identify by itself. A variety of diagnosability models have been suggested. It turns out that a diagnosability property of a network structure is closely associated with its relevant connectivity property. Based on this observation, a general diagnosability derivation process has been suggested. The g-extra connectivity of a graph G characterizes the size of a minimum vertex set F such that, when it is removed, every component in the disconnected survival graph, contains at least g + 1 vertices. In this paper, we discuss the aforementioned general derivation process, derive the g-extra connectivity, and then apply the aforementioned general process to reveal the g-extra diagnosability of the generalized exchanged hypercube.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"8 1","pages":"112 - 123"},"PeriodicalIF":0.8,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90777096","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 : 2020-04-02DOI: 10.1080/23799927.2020.1761886
A. Khamseh
Given t distinct colors, we order the t subsets of t−1 colors in some arbitrary manner. Let be graphs. The -chromatic Ramsey number, denoted by , is defined to be the least number n such that if the edges of the complete graph are colored in any fashion with t colors, then for some i the subgraph whose edges are colored with the ith subset of colors contains a . In this paper, we study the -chromatic Ramsey number of linear forests.
{"title":"A note on (t - 1)-chromatic Ramsey number of linear forests","authors":"A. Khamseh","doi":"10.1080/23799927.2020.1761886","DOIUrl":"https://doi.org/10.1080/23799927.2020.1761886","url":null,"abstract":"Given t distinct colors, we order the t subsets of t−1 colors in some arbitrary manner. Let be graphs. The -chromatic Ramsey number, denoted by , is defined to be the least number n such that if the edges of the complete graph are colored in any fashion with t colors, then for some i the subgraph whose edges are colored with the ith subset of colors contains a . In this paper, we study the -chromatic Ramsey number of linear forests.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"24 1","pages":"92 - 97"},"PeriodicalIF":0.8,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83262029","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 : 2020-04-02DOI: 10.1080/23799927.2020.1762744
James Hallas, Maria Talanda-Fisher, Ping Zhang
A vertex v in a graph G is said to dominate a vertex u if either u = v or and a set S of vertices in G is a dominating set of G if every vertex of G is dominated by at least one vertex in S. Domination has been looked at in an equivalent way. A function is a dominating function of a graph G if for every vertex v of G. We use dominating functions to investigate graphs all of whose vertices are dominated by the same number of vertices as well as those graphs whose vertices are dominated by as many different number of vertices as possible.
{"title":"Dominating functions in graphs – regularity versus irregularity","authors":"James Hallas, Maria Talanda-Fisher, Ping Zhang","doi":"10.1080/23799927.2020.1762744","DOIUrl":"https://doi.org/10.1080/23799927.2020.1762744","url":null,"abstract":"A vertex v in a graph G is said to dominate a vertex u if either u = v or and a set S of vertices in G is a dominating set of G if every vertex of G is dominated by at least one vertex in S. Domination has been looked at in an equivalent way. A function is a dominating function of a graph G if for every vertex v of G. We use dominating functions to investigate graphs all of whose vertices are dominated by the same number of vertices as well as those graphs whose vertices are dominated by as many different number of vertices as possible.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"14 1","pages":"111 - 98"},"PeriodicalIF":0.8,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80815360","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 : 2020-02-26DOI: 10.1080/23799927.2020.1735523
Hong Zhang, Laijiang Zhang, J. Meng
Diagnosabilty is an important metric to the capability of fault identification for multiprocessor systems. However, most researches on diagnosability focus on vertex fault. In real circumstances, not only vertex faults take place but also malfunctions may arise. In this paper, we study the diagnosability of k-regular 2-cn graph with missing edges. Let be a set of missing edges in graph G with . We prove that the diagnosability of is at most for . Furthermore, we obtain that the worst-case diagnosability (h-edge tolerable diagnosability), denoted by , is maximum number of faulty nodes that a system G can guarantee to locate when the number of faulty links does not exceed h. As applications, the diagnosabilities of many networks with missing edges are determined under the PMC model.
{"title":"Hybrid fault diagnosis capability analysis of regular graphs under the PMC model","authors":"Hong Zhang, Laijiang Zhang, J. Meng","doi":"10.1080/23799927.2020.1735523","DOIUrl":"https://doi.org/10.1080/23799927.2020.1735523","url":null,"abstract":"Diagnosabilty is an important metric to the capability of fault identification for multiprocessor systems. However, most researches on diagnosability focus on vertex fault. In real circumstances, not only vertex faults take place but also malfunctions may arise. In this paper, we study the diagnosability of k-regular 2-cn graph with missing edges. Let be a set of missing edges in graph G with . We prove that the diagnosability of is at most for . Furthermore, we obtain that the worst-case diagnosability (h-edge tolerable diagnosability), denoted by , is maximum number of faulty nodes that a system G can guarantee to locate when the number of faulty links does not exceed h. As applications, the diagnosabilities of many networks with missing edges are determined under the PMC model.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"72 1","pages":"61 - 71"},"PeriodicalIF":0.8,"publicationDate":"2020-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81217037","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 : 2020-01-29DOI: 10.1080/23799927.2020.1842808
D. Grigoriev, V. Shpilrain
A blockchain is redactable if a private key holder (e.g. a central authority) can change any single block without violating integrity of the whole blockchain, but no other party can do that. In this paper, we offer a simple method of constructing redactable blockchains inspired by the ideas underlying the well-known RSA encryption scheme. Notably, our method can be used in conjunction with any reasonable hash function that is used to build a blockchain. Public immutability of a blockchain in our construction is based on the computational hardness of the RSA problem and not on properties of the underlying hash function. Corruption resistance is based on the computational hardness of the discrete logarithm problem.
{"title":"RSA and redactable blockchains","authors":"D. Grigoriev, V. Shpilrain","doi":"10.1080/23799927.2020.1842808","DOIUrl":"https://doi.org/10.1080/23799927.2020.1842808","url":null,"abstract":"A blockchain is redactable if a private key holder (e.g. a central authority) can change any single block without violating integrity of the whole blockchain, but no other party can do that. In this paper, we offer a simple method of constructing redactable blockchains inspired by the ideas underlying the well-known RSA encryption scheme. Notably, our method can be used in conjunction with any reasonable hash function that is used to build a blockchain. Public immutability of a blockchain in our construction is based on the computational hardness of the RSA problem and not on properties of the underlying hash function. Corruption resistance is based on the computational hardness of the discrete logarithm problem.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"12 1","pages":"1 - 6"},"PeriodicalIF":0.8,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84714900","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 : 2020-01-02DOI: 10.1080/23799927.2020.1723708
Elham Abdali, R. Fallahnejad
Conventional data envelopment analysis (DEA) is a method for measuring the efficiency of decision-making units (DMUs). Recently, to measure the efficiency of sub-DMUs (Stages), several network DEA models have been developed, in which the results of network DEA models not only provide the overall efficiency of the whole system but also provide the efficiency of the individual stages. This study develops a bargaining game model for measuring the efficiency of DMUs that have a two-stage network structure with non-discretionary inputs, that the model as a method of dealing with the conflict arising from the intermediate measures. Under the Nash bargaining game theory, the two stages in the network DEA are considered as players and network DEA model is a cooperative game model. Here, the non-discretionary additional inputs in the second stage make changes in the cooperative game model, so that managers of units cannot change the value of non-discretionary inputs in measuring the efficiency of the bargaining game model, and this causes the desired and expected output of the managers not to be produced. In addition, it can be stated that the presence of such inputs is capable, significantly affecting the system efficiency score and stages. So that the existence of the inputs in the measuring efficiency of decision-making units reduces the efficiency score of cooperative game. In this study, linearizing the model in the presence of the non-discretionary input is a new idea in the bargaining game model. A numerical example shows the applicability of the new model.
{"title":"A bargaining game model for measuring efficiency of two-stage network DEA with non-discretionary inputs","authors":"Elham Abdali, R. Fallahnejad","doi":"10.1080/23799927.2020.1723708","DOIUrl":"https://doi.org/10.1080/23799927.2020.1723708","url":null,"abstract":"Conventional data envelopment analysis (DEA) is a method for measuring the efficiency of decision-making units (DMUs). Recently, to measure the efficiency of sub-DMUs (Stages), several network DEA models have been developed, in which the results of network DEA models not only provide the overall efficiency of the whole system but also provide the efficiency of the individual stages. This study develops a bargaining game model for measuring the efficiency of DMUs that have a two-stage network structure with non-discretionary inputs, that the model as a method of dealing with the conflict arising from the intermediate measures. Under the Nash bargaining game theory, the two stages in the network DEA are considered as players and network DEA model is a cooperative game model. Here, the non-discretionary additional inputs in the second stage make changes in the cooperative game model, so that managers of units cannot change the value of non-discretionary inputs in measuring the efficiency of the bargaining game model, and this causes the desired and expected output of the managers not to be produced. In addition, it can be stated that the presence of such inputs is capable, significantly affecting the system efficiency score and stages. So that the existence of the inputs in the measuring efficiency of decision-making units reduces the efficiency score of cooperative game. In this study, linearizing the model in the presence of the non-discretionary input is a new idea in the bargaining game model. A numerical example shows the applicability of the new model.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"694 1","pages":"48 - 59"},"PeriodicalIF":0.8,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80581884","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 : 2020-01-02DOI: 10.1080/23799927.2019.1708465
Yufei Huang, Weihua He, Guixian Huang, H. Lai, Sulin Song
The line graph of a graph G is a simple graph with being its vertex set, where two vertices are adjacent in whenever the corresponding edges share a common vertex in G. A graph H is even if every vertex of H has even degree, and a graph is supereulerian if it has a spanning closed trail. We obtain a characterization for a graph G to have a supereulerian line graph , as follows: for a connected graph G with , the line graph has a spanning closed trail if and only if G has an even subgraph H (possibly null) such that both G remains connected after deleting all degree 2 vertices not in H, and every degree 2 vertex not in H must be adjacent only to vertices of degree at least 3 in G.
{"title":"A characterization of graphs with supereulerian line graphs","authors":"Yufei Huang, Weihua He, Guixian Huang, H. Lai, Sulin Song","doi":"10.1080/23799927.2019.1708465","DOIUrl":"https://doi.org/10.1080/23799927.2019.1708465","url":null,"abstract":"The line graph of a graph G is a simple graph with being its vertex set, where two vertices are adjacent in whenever the corresponding edges share a common vertex in G. A graph H is even if every vertex of H has even degree, and a graph is supereulerian if it has a spanning closed trail. We obtain a characterization for a graph G to have a supereulerian line graph , as follows: for a connected graph G with , the line graph has a spanning closed trail if and only if G has an even subgraph H (possibly null) such that both G remains connected after deleting all degree 2 vertices not in H, and every degree 2 vertex not in H must be adjacent only to vertices of degree at least 3 in G.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"11 1","pages":"1 - 14"},"PeriodicalIF":0.8,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78935084","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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