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Soonhak Kwon - One of the best experts on this subject based on the ideXlab platform.
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a refinement of muller s cube Root Algorithm
Finite Fields and Their Applications, 2020Co-Authors: Soonhak KwonAbstract:Abstract Let p be a prime such that p ≡ 1 ( mod 3 ) . Let c be a cubic residue ( mod p ) such that c p − 1 3 ≡ 1 ( mod p ) . In this paper, we present a refinement of Muller's Algorithm for computing a cube Root of c [11] , which also improves Williams' [14] , [15] Cipolla-Lehmer type Algorithms. Under the assumption that a suitable irreducible polynomial of degree 3 is given, Muller gave a cube Root Algorithm which requires 8.5 log p modular multiplications. Our Algorithm requires only 7.5 log p modular multiplications and is based on the recurrence relations arising from the irreducible polynomial h ( x ) = x 3 + c t 3 x − c t 3 for some integer t.
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new cube Root Algorithm based on the third order linear recurrence relations in finite fields
Designs Codes and Cryptography, 2015Co-Authors: Eunhye Ha, Soonhak KwonAbstract:In this paper, we present a new cube Root Algorithm in the finite field $$\mathbb {F}_{q}$$ F q with $$q$$ q a power of prime, which extends the Cipolla---Lehmer type Algorithms (Cipolla, Un metodo per la risolutione della congruenza di secondo grado, 1903; Lehmer, Computer technology applied to the theory of numbers, 1969). Our cube Root method is inspired by the work of Muller (Des Codes Cryptogr 31:301---312, 2004) on the quadratic case. For a given cubic residue $$c \in \mathbb {F}_{q}$$ c ? F q with $$q \equiv 1 \pmod {9}$$ q ? 1 ( mod 9 ) , we show that there is an irreducible polynomial $$f(x)$$ f ( x ) with Root $$\alpha \in \mathbb {F}_{q^{3}}$$ ? ? F q 3 such that $$Tr\left( \alpha ^{\frac{q^{2}+q-2}{9}}\right) $$ T r ? q 2 + q - 2 9 is a cube Root of $$c$$ c . Consequently we find an efficient cube Root Algorithm based on the third order linear recurrence sequences arising from $$f(x)$$ f ( x ) . The complexity estimation shows that our Algorithm is better than the previously proposed Cipolla---Lehmer type Algorithms.
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remarks on the pocklington and padro saez cube Root Algorithm in f q
Electronics Letters, 2014Co-Authors: Seokhwan Choi, Soonhak KwonAbstract:A cube Root Algorithm in
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Remarks on the Pocklington and Padró-Sáez Cube Root Algorithm in 𝔽 q .
IACR Cryptology ePrint Archive, 2014Co-Authors: Geon Heo, Seokhwan Choi, Kwang Ho Lee, Namhun Koo, Soonhak KwonAbstract:We clarify and generalize a cube Root Algorithm in Fq proposed by Pocklington [1], and later rediscovered by Padro and Saez [2]. We correct some mistakes in [2] and give a full generalization of the result in [1, 2] for the cube Root Algorithm. We also give the comparison of the implementation of Pocklington and Padro-Saez Algorithm with two most popular cube Root Algorithms, namely the Adleman-Manders-Miller Algorithm and the Cipolla-Lehmer Algorithm. To the authors’ knowledge, our comparison is the first one which compares three fundamental Algorithms together.
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Remarks on the Pocklington and Padró–Sáez cube Root Algorithm in q
Electronics Letters, 2014Co-Authors: Geon Heo, Seokhwan Choi, Kwang Ho Lee, Namhun Koo, Soonhak KwonAbstract:A cube Root Algorithm in
Diego Oliva - One of the best experts on this subject based on the ideXlab platform.
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An improved runner-Root Algorithm for solving feature selection problems based on rough sets and neighborhood rough sets
Applied Soft Computing, 2020Co-Authors: Rehab Ali Ibrahim, Mohamed Abd Elaziz, Diego OlivaAbstract:Abstract Solving the feature selection problem is considered an important issue when addressing data from real applications that contain a large number of features. However, not all of these features are important; therefore, the redundant features must be removed because they affect the accuracy of the data representation and introduce time complexity into the analysis of these data. For these reasons, the feature selection problem is considered an NP-complete nonlinearly constrained optimization problem. The rough set (RS) and neighborhood rough set (NRS) are the most powerful methods used to solve the feature selection problem; however, both approaches suffer from high time complexity. To avoid these limitations, we combined the RS and NRS with a new metaheuristic Algorithm called the runner-Root Algorithm (RRA). The spirit of the RRA originated from real-life plants called running plants, which have Roots and runners that spread the plants in search of minerals and water resources through their Root and runner development. To validate the proposed Algorithm, several UCI Machine Learning Repository datasets are used to compute the performance of our Algorithm employing two effective classifiers, the random forest and the K-nearest neighbor, in addition to some other measures for the performance evaluation. The experimental results illustrate that the proposed Algorithm is superior to the state-of-the-art metaheuristic Algorithms in terms of the performance measures. Additionally, the NRS increases the performance of the proposed method more than the RS as an objective function.
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feature selection based on improved runner Root Algorithm using chaotic singer map and opposition based learning
International Conference on Neural Information Processing, 2017Co-Authors: Rehab Ali Ibrahim, Diego Oliva, Ahmed A EweesAbstract:The feature selection (FS) is an important step for data analysis. FS is used to reduce the dimension of data by selecting the relevant features; while removing the redundant, noisy and irrelevant features that lead to degradation of the performance. Several swarm techniques are used to solve the FS problem and these methods provide results better than classical approaches. However, most of these techniques have limitations such as slow convergence and time complexity. These limitations occur due that all the agents update their position according to the best one. However, this best agent may be not the optimal global solution for FS, therefore, the swarm getting stuck in a local solution. This paper proposes an improved Runner-Root Algorithm (RRA). The RRA is combined with chaotic Singer map and opposition-based learning to increase its accuracy. The experiments are performed in eight datasets and the performance of the proposed method is compared against swarm Algorithms.
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ICONIP (5) - Feature Selection Based on Improved Runner-Root Algorithm Using Chaotic Singer Map and Opposition-Based Learning
Neural Information Processing, 2017Co-Authors: Rehab Ali Ibrahim, Diego Oliva, Ahmed A EweesAbstract:The feature selection (FS) is an important step for data analysis. FS is used to reduce the dimension of data by selecting the relevant features; while removing the redundant, noisy and irrelevant features that lead to degradation of the performance. Several swarm techniques are used to solve the FS problem and these methods provide results better than classical approaches. However, most of these techniques have limitations such as slow convergence and time complexity. These limitations occur due that all the agents update their position according to the best one. However, this best agent may be not the optimal global solution for FS, therefore, the swarm getting stuck in a local solution. This paper proposes an improved Runner-Root Algorithm (RRA). The RRA is combined with chaotic Singer map and opposition-based learning to increase its accuracy. The experiments are performed in eight datasets and the performance of the proposed method is compared against swarm Algorithms.
Rehab Ali Ibrahim - One of the best experts on this subject based on the ideXlab platform.
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An improved runner-Root Algorithm for solving feature selection problems based on rough sets and neighborhood rough sets
Applied Soft Computing, 2020Co-Authors: Rehab Ali Ibrahim, Mohamed Abd Elaziz, Diego OlivaAbstract:Abstract Solving the feature selection problem is considered an important issue when addressing data from real applications that contain a large number of features. However, not all of these features are important; therefore, the redundant features must be removed because they affect the accuracy of the data representation and introduce time complexity into the analysis of these data. For these reasons, the feature selection problem is considered an NP-complete nonlinearly constrained optimization problem. The rough set (RS) and neighborhood rough set (NRS) are the most powerful methods used to solve the feature selection problem; however, both approaches suffer from high time complexity. To avoid these limitations, we combined the RS and NRS with a new metaheuristic Algorithm called the runner-Root Algorithm (RRA). The spirit of the RRA originated from real-life plants called running plants, which have Roots and runners that spread the plants in search of minerals and water resources through their Root and runner development. To validate the proposed Algorithm, several UCI Machine Learning Repository datasets are used to compute the performance of our Algorithm employing two effective classifiers, the random forest and the K-nearest neighbor, in addition to some other measures for the performance evaluation. The experimental results illustrate that the proposed Algorithm is superior to the state-of-the-art metaheuristic Algorithms in terms of the performance measures. Additionally, the NRS increases the performance of the proposed method more than the RS as an objective function.
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feature selection based on improved runner Root Algorithm using chaotic singer map and opposition based learning
International Conference on Neural Information Processing, 2017Co-Authors: Rehab Ali Ibrahim, Diego Oliva, Ahmed A EweesAbstract:The feature selection (FS) is an important step for data analysis. FS is used to reduce the dimension of data by selecting the relevant features; while removing the redundant, noisy and irrelevant features that lead to degradation of the performance. Several swarm techniques are used to solve the FS problem and these methods provide results better than classical approaches. However, most of these techniques have limitations such as slow convergence and time complexity. These limitations occur due that all the agents update their position according to the best one. However, this best agent may be not the optimal global solution for FS, therefore, the swarm getting stuck in a local solution. This paper proposes an improved Runner-Root Algorithm (RRA). The RRA is combined with chaotic Singer map and opposition-based learning to increase its accuracy. The experiments are performed in eight datasets and the performance of the proposed method is compared against swarm Algorithms.
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ICONIP (5) - Feature Selection Based on Improved Runner-Root Algorithm Using Chaotic Singer Map and Opposition-Based Learning
Neural Information Processing, 2017Co-Authors: Rehab Ali Ibrahim, Diego Oliva, Ahmed A EweesAbstract:The feature selection (FS) is an important step for data analysis. FS is used to reduce the dimension of data by selecting the relevant features; while removing the redundant, noisy and irrelevant features that lead to degradation of the performance. Several swarm techniques are used to solve the FS problem and these methods provide results better than classical approaches. However, most of these techniques have limitations such as slow convergence and time complexity. These limitations occur due that all the agents update their position according to the best one. However, this best agent may be not the optimal global solution for FS, therefore, the swarm getting stuck in a local solution. This paper proposes an improved Runner-Root Algorithm (RRA). The RRA is combined with chaotic Singer map and opposition-based learning to increase its accuracy. The experiments are performed in eight datasets and the performance of the proposed method is compared against swarm Algorithms.
Ahmed A Ewees - One of the best experts on this subject based on the ideXlab platform.
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feature selection based on improved runner Root Algorithm using chaotic singer map and opposition based learning
International Conference on Neural Information Processing, 2017Co-Authors: Rehab Ali Ibrahim, Diego Oliva, Ahmed A EweesAbstract:The feature selection (FS) is an important step for data analysis. FS is used to reduce the dimension of data by selecting the relevant features; while removing the redundant, noisy and irrelevant features that lead to degradation of the performance. Several swarm techniques are used to solve the FS problem and these methods provide results better than classical approaches. However, most of these techniques have limitations such as slow convergence and time complexity. These limitations occur due that all the agents update their position according to the best one. However, this best agent may be not the optimal global solution for FS, therefore, the swarm getting stuck in a local solution. This paper proposes an improved Runner-Root Algorithm (RRA). The RRA is combined with chaotic Singer map and opposition-based learning to increase its accuracy. The experiments are performed in eight datasets and the performance of the proposed method is compared against swarm Algorithms.
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ICONIP (5) - Feature Selection Based on Improved Runner-Root Algorithm Using Chaotic Singer Map and Opposition-Based Learning
Neural Information Processing, 2017Co-Authors: Rehab Ali Ibrahim, Diego Oliva, Ahmed A EweesAbstract:The feature selection (FS) is an important step for data analysis. FS is used to reduce the dimension of data by selecting the relevant features; while removing the redundant, noisy and irrelevant features that lead to degradation of the performance. Several swarm techniques are used to solve the FS problem and these methods provide results better than classical approaches. However, most of these techniques have limitations such as slow convergence and time complexity. These limitations occur due that all the agents update their position according to the best one. However, this best agent may be not the optimal global solution for FS, therefore, the swarm getting stuck in a local solution. This paper proposes an improved Runner-Root Algorithm (RRA). The RRA is combined with chaotic Singer map and opposition-based learning to increase its accuracy. The experiments are performed in eight datasets and the performance of the proposed method is compared against swarm Algorithms.
Thuan Thanh Nguyen - One of the best experts on this subject based on the ideXlab platform.
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Electric distribution network reconfiguration for power loss reduction based on runner Root Algorithm
International Journal of Electrical and Computer Engineering (IJECE), 2020Co-Authors: Thuan Thanh NguyenAbstract:This paper proposes a method for solving the distribution network reconfiguration (NR) problem based on runner Root Algorithm (RRA) for reducing active power loss. The RRA is a recent developed metaheuristic Algorithm inspired from runners and Roots of plants to search water and minerals. RRA is equipped with four tools for searching the optimal solution. In which, the random jumps and the restart of population are used for exploring and the elite selection and random jumps around the current best solution are used for exploiting. The effectiveness of the RRA is evaluated on the 16 and 69-node system. The obtained results are compared with particle swarm optimization and other methods. The numerical results show that the RRA is the potential method for the NR problem.
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Two States for Optimal Position and Capacity of Distributed Generators Considering Network Reconfiguration for Power Loss Minimization Based on Runner Root Algorithm
Energies, 2018Co-Authors: Anh Viet Truong, Thuan Thanh Nguyen, Trieu Ngoc Ton, Thanh Long DuongAbstract:Although the distributed generator (DG) placement and distribution network (DN) reconfiguration techniques contribute to reduce power loss, obviously the former is a design problem which is used for a long-term purpose while the latter is an operational problem which is used for a short-term purpose. In this situation, the optimal value of the position and capacity of DGs is a value which must be not affected by changing the operational configuration due to easy changes in the status of switches compared with changes in the installed location of DG. This paper demonstrates a methodology for choosing the position and size of DGs on the DN that takes into account re-switching the status of switches on distribution of the DN to reduce power losses. The proposed method is based on the runner Root Algorithm (RRA) which separates the problem into two states. In State-I, RRA is used to optimize the position and size of DGs on closed-loop distribution networks which is a mesh shape topology and power is delivered through more than one line. In State-II, RRA is used to reconfigure the DN after placing the DGs to find the open-loop distribution network which is a tree shape topology and power is only delivered through one line. The calculation results in DN systems with 33 nodes and 69 nodes, showing that the proposed method is capable of solving the problem of the optimal position and size of DGs considering distribution network reconfiguration.
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multi objective electric distribution network reconfiguration solution using runner Root Algorithm
Applied Soft Computing, 2017Co-Authors: Thuan Thanh Nguyen, Thang Trung Nguyen, Anh Viet Truong, Quyen Thi Nguyen, Tuan Anh PhungAbstract:Display Omitted The runner-Root Algorithm (RRA) is adapted to solve the network reconfiguration problem.Five objectives namely power loss, load balancing among the branches, load balancing among the feeders, number of switching operations and node voltage deviation are considered.The proposed RRA method is applied to the 33-bus and 70-bus test networks for evaluation.The proposed RRA method has better performance in comparison to other methods. This paper presents a runner-Root Algorithm (RRA) for electric distribution network reconfiguration (NR) problem. The considered NR problem in this paper is to minimize real power loss, load balancing among the branches, load balancing among the feeders as well as number of switching operations and node voltage deviation using max-min method for selection of the final compromised solution. RRA is equipped with two explorative tools, which are random jumps with large steps and re-initialization strategy to escape from local optimal. Moreover, RRA is also equipped with an exploitative tool to search around the current best solution with large and small steps to ensure the obtained result of global optimization. The effectiveness of the applied RRA in both single- and multi-objective has been tested on 33-node and 70-node distribution network systems and the obtained test results have been compared to those from other methods in the literature. The simulation results show that the applied RRA can be an efficient method for network reconfiguration problems with single- and multi-objective.
