Simple method to extract minimal cut sets of a direct network
*Roaa Aziz FadhilCorresponding authorroaaazizfadhil@gmail.comroaa.fadhil.pure256@student.uobabylon.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonBabil, IraqView full profile → , Zahir Al-Khafajimathzahir@gmail.comDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonBabil, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 11 May 2022
- Accepted:
- 08 Jun 2022
- Published Online:
- 15 Jul 2023
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1527
- Pages:
- 903–908
Abstract
Keywords
Subject Classifications
Acknowledgements
References
[1] Abbas, S.A.K., Haddi Hassan, Z. A., “Increase the Reliability of Critical Units by Using Redundant Technologies”, Journal of Physics: Conference Series, 1999(1) 012107 (2021).
[2] Abbas, S.A.K., Hassan, Z. A. H., “Use of ARINC Approach method to evaluate the reliability assignment for mixed system”, Journal of Physics: Conference Series, 1999(1) 012102 (2021).
[3] Abd Alsharify, F. H., Haddi Hassan, Z. A., “Computing the reliability of a complex network using two techniques”, Journal of Physics: Conference Series, 1963(1) 012016 (2021).
[4] Abd Alsharify, F.H., Mudhar, G.A., Haddi Hassan, Z. A., “A modified technique to compute the minimal path sets for the reliability of complex network”, Journal of Physics: Conference Series, 1999(1) 012083 (2021).
[5] Ameer issa, L. A. A., Haddi Hassan, Z. A., “Use of a modified Markov models for parallel reliability systems that are subject to
maintenance”, Journal of Physics: Conference Series, 1999(1) 012087 (2021).
[6] Dwail H H et al., A new modified TR algorithm with adaptive radius to solve a nonlinear systems of equations, J. Phys.: Conf. Ser. 1804 012108 (2021).
[7] Fathabadi, H. Salehi, et al., “Determining all minimal paths of a network”, Australian Journal of Basic and Applied Sciences 3.4, 3771-3777 (2009).
[8] Hashim K H and Shiker M A K. Using a new line search method with gradient direction to solve nonlinear systems of equations, J. Phys.: Conf. Ser. 1804 012106 (2021).
[9] K. D. Heidtmann, “Inverting paths and cuts of 2-state system”, IEEE Trans. Reliability”, vol R-32, pp 469- 471, 474 (1983).
[10] Mahdi M M et al., Solving systems of nonlinear monotone equations by using a new projection approach, J. Phys.: Conf. Ser. 1804 012107 (2021).
[11] M. O. Locks, “Inverting and minimalizing path sets and cut sets”, IEEE Trans. Reliability, Vol. R-27, pp 107-109 (1978 Jun).
[12] M. O. Locks, “Inverting and minimalizing Boolean functions minimal paths and minimal cuts non coherent system analysis”, IEEE Trans. Reliability, Vol R-28, pp 373-375 (1979).
[13] S. Rai, “Comments on Inverting and minimalizing path sets and cut Sets”, IEEE Trans. Reliability, Vol R-28, p 263 (1979).
[14] S. Rai and K.K. Aggarwal, “On complementation of path sets and Cutsets”. IEEE Transactions on Reliability, 29, 139-140 (1980).
[15] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guideto the Theory of NP-hardness, E.H. Freeman (1979).
[16] Y. Shen, “A New Simple Algorithm for Enumerating all Minimal Paths and Cuts of a Graph,” Microelectronics and Reliability, Vol. 35, no. 6, pp. 973–976 (1995).
[17] W. Yeh, “A new approach to evaluate reliability of multistate networks under the cost constraint,” Omega, Vol. 33, pp. 203–209 (2005).
[18] Yeh, W. C. A simple algorithm to search for all MCs networks. European Journal of Operational Research, 174(3), 1694-1705 (2006).
[19] Yeh, W. C. A simple algorithm for evaluating the k-out-of-n network reliability. Reliability Engineering & System Safety, 83(1), 93-101 (2004).
[20] Zhu, Wenbo, et al. “A new node-based concept for solving the minimal path problem in general networks”, IEEE Access 7: 173310-173319 (2019).
[21] Shubham Sharma & Ahmed J. Obaid. Mathematical modelling, analysis and design of fuzzy logic controller for the control of ventilation systems using MATLAB fuzzy logic toolbox, Journal of Interdisciplinary Mathematics, 23:4, 843-849 (2020), DOI: 10.1080/09720502.2020.1727611
[22] Stefan M. Stefanov. Valid inequalities, cutting planes and integrality of the knapsack polytope, Journal of Interdisciplinary Mathematics, 14:4, 389-406 (2011), DOI: 10.1080/09720502.2011.10700759.




