Search results for: Soliton solution
2523 Soliton Interaction in Multi-Core Optical Fiber: Application to WDM System
Authors: S. Arun Prakash, V. Malathi, M. S. Mani Rajan
Abstract:The analytical bright two soliton solution of the 3- coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two-soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.
Keywords: Optical soliton, soliton interaction, soliton switching, WDM.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1860
2522 Instability of Soliton Solutions to the Schamel-nonlinear Schrödinger Equation
Authors: Sarun Phibanchon, Michael A. Allen
A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schr┬¿odinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton.
Keywords: Soliton, instability, variational method, spectral method.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3529
2521 Some Exact Solutions of the (2+1)-Dimensional Breaking Soliton Equation using the Three-wave Method
Authors: Mohammad Taghi Darvishi, Mohammad Najafi
This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward.
Keywords: Soliton solution, computerized symbolic computation, painleve analysis, (2+1)-dimensional breaking soliton equation, Hirota's bilinear form.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1772
2520 Characteristic Study on Conventional and Soliton Based Transmission System
Authors: Bhupeshwaran Mani, S. Radha, A. Jawahar, A. Sivasubramanian
Abstract:Here, we study the characteristic feature of conventional (ON-OFF keying) and soliton based transmission system. We consider 20Gbps transmission system implemented with Conventional Single Mode Fiber (C-SMF) to examine the role of Gaussian pulse which is the characteristic of conventional propagation and Hyperbolic-secant pulse which is the characteristic of soliton propagation in it. We note the influence of these pulses with respect to different dispersion lengths and soliton period in conventional and soliton system respectively and evaluate the system performance in terms of Quality factor. From the analysis, we could prove that the soliton pulse has the consistent performance even for long distance without dispersion compensation than the conventional system as it is robust to dispersion. For the length of transmission of 200Km, soliton system yielded Q of 33.958 while the conventional system totally exhausted with Q=0.
Keywords: Soliton, dispersion length, Soliton period, Return-tozero (RZ), Q-factor.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1515
2519 Extend Three-wave Method for the (3+1)-Dimensional Soliton Equation
Authors: Somayeh Arbabi Mohammad-Abadi, Maliheh Najafi
In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota-s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented.
Keywords: Three-wave method, (3+1)-dimensional Soliton equation, Hirota's bilinear form.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1442
2518 Multiple Soliton Solutions of (2+1)-dimensional Potential Kadomtsev-Petviashvili Equation
Authors: Mohammad Najafi, Ali Jamshidi
We employ the idea of Hirota-s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.
Keywords: Hirota bilinear method, potential Kadomtsev-Petviashvili equation, multiple soliton solutions, multiple singular soliton solutions.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1262
2517 Realization of Soliton Phase Characteristics in 10 Gbps, Single Channel, Uncompensated Telecommunication System
Authors: A. Jawahar
Abstract:In this paper, the dependence of soliton pulses with respect to phase in a 10Gbps, single channel, dispersion uncompensated telecommunication system was studied. The characteristic feature of periodic soliton interaction was noted at the Interaction point (I=6202.5Km) in one collision length of L=12405.1 Km. The interaction point is located for 10Gbps system with an initial relative spacing (qo) of soliton as 5.28 using Perturbation theory. It is shown that, when two in-phase solitons are launched, they interact at the point I=6202.5 Km, but the interaction could be restricted with introduction of different phase initially. When the phase of the input solitons increases, the deviation of soliton pulses at the ‘I’ also increases. We have successfully demonstrated this effect in a telecommunication set-up in terms of Quality factor (Q), where the Q=0 for in-phase soliton. The Q was noted to be 125.9, 38.63, 47.53, 59.60, 161.37, and 78.04 for different phases such as 10o, 20o, 30o, 45o, 60o and 90o degrees respectively at Interaction point (I).
Keywords: Soliton interaction, Initial relative spacing, phase, Perturbation theory and telecommunication system.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1697
2516 Optical Switching Based On Bragg Solitons in A Nonuniform Fiber Bragg Grating
Authors: Abdulatif Abdusalam, Mohamed Shaban
In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We then discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.
Keywords: Bragg grating, Nonuniform fiber, Nonlinear pulse.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1782
2515 New Exact Solutions for the (3+1)-Dimensional Breaking Soliton Equation
Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi
In this work, we obtain some analytic solutions for the (3+1)-dimensional breaking soliton after obtaining its Hirota-s bilinear form. Our calculations show that, three-wave method is very easy and straightforward to solve nonlinear partial differential equations.
Keywords: (3+1)-dimensional breaking soliton equation, Hirota'sbilinear form.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1542
2514 Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method
Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi
In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.
Keywords: Exact solution, The (3+1)-dimensional breaking soliton equation, ( G G )-expansion method, Riccati equation, Modified Fexpansion method.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2588
2513 The Direct Ansaz Method for Finding Exact Multi-Wave Solutions to the (2+1)-Dimensional Extension of the Korteweg de-Vries Equation
Authors: Chuanjian Wang, Changfu Liu, Zhengde Dai
In this paper, the direct AnsAz method is used for constructing the multi-wave solutions to the (2+1)-dimensional extension of the Korteweg de-Vries (shortly EKdV) equation. A new breather type of three-wave solutions including periodic breather type soliton solution, breather type of two-solitary solution are obtained. Some cases with specific values of the involved parameters are plotted for each of the three-wave solutions. Mechanical features of resonance interaction among the multi-wave are discussed. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.
Keywords: EKdV equation, Breather, Soliton, Bilinear form, The direct AnsAz method.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1455
2512 Exact Pfaffian and N-Soliton Solutions to a (3+1)-Dimensional Generalized Integrable Nonlinear Partial Differential Equations
Authors: Magdy G. Asaad
Abstract:The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N-soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.
Keywords: Bilinear operator, G-BKP equation, Integrable nonlinear PDEs, Jimbo-Miwa equation, Ma-Fan equation, N-soliton solutions, Pfaffian solutions.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1948
2511 Two-Dimensional Solitary Wave Solution to the Quadratic Nonlinear Schrdinger Equation
Authors: Sarun Phibanchon
The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.
Keywords: soliton, iterative method, spectral method, plasmaProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1744
2510 Soliton Interaction in Birefringent Fibers with Third-Order Dispersion
Authors: Dowluru Ravi Kumar, Bhima Prabhakara Rao
Propagation of solitons in single-mode birefringent fibers is considered under the presence of third-order dispersion (TOD). The behavior of two neighboring solitons and their interaction is investigated under the presence of third-order dispersion with different group velocity dispersion (GVD) parameters. It is found that third-order dispersion makes the resultant soliton to deviate from its ideal position and increases the interaction between adjacent soliton pulses. It is also observed that this deviation due to third-order dispersion is considerably small when the optical pulse propagates at wavelengths relatively far from the zerodispersion. Modified coupled nonlinear Schrödinger-s equations (CNLSE) representing the propagation of optical pulse in single mode fiber with TOD are solved using split-step Fourier algorithm. The results presented in this paper reveal that the third-order dispersion can substantially increase the interaction between the solitons, but large group velocity dispersion reduces the interaction between neighboring solitons.
Keywords: Birefringence, Group velocity dispersion, Polarization mode dispersion, Soliton interaction, Third order dispersion.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1107
2509 New Application of EHTA for the Generalized(2+1)-Dimensional Nonlinear Evolution Equations
Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi
In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.
Keywords: EHTA, (2+1)-dimensional CBS equations, (2+1)-dimensional breaking solution equation, Hirota's bilinear form.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1341
2508 New Exact Three-Wave Solutions for the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov System
Authors: Fadi Awawdeh, O. Alsayyed
New exact three-wave solutions including periodic two-solitary solutions and doubly periodic solitary solutions for the (2+1)-dimensional asymmetric Nizhnik-Novikov- Veselov (ANNV) system are obtained using Hirota's bilinear form and generalized three-wave type of ansatz approach. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an e¤ective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.
Keywords: Soliton Solution, Hirota Bilinear Method, ANNV System.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1389
2507 An Asymptotic Solution for the Free Boundary Parabolic Equations
Authors: Hsuan-Ku Liu, Ming Long Liu
In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.
Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1358
2506 On the Approximate Solution of a Nonlinear Singular Integral Equation
Authors: Nizami Mustafa, C. Ardil
In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.
Keywords: Approximate solution, Fixed-point principle, Nonlinear singular integral equations, Vekua integral operatorProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1740
2505 Laplace Decomposition Approximation Solution for a System of Multi-Pantograph Equations
Authors: M. A. Koroma, C. Zhan, A. F. Kamara, A. B. Sesay
In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.
Keywords: Laplace decomposition, pantograph equations, exact solution, numerical solution, approximate solution.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1507
2504 Numerical Study of a Class of Nonlinear Partial Differential Equations
Authors: Kholod M. Abu-Alnaja
Abstract:In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.
Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential EquationsProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1345
2503 Solution of Fuzzy Differential Equation under Generalized Differentiability by Genetic Programming
Authors: N. Kumaresan, J. Kavikumar, M. Kumudthaa, Kuru Ratnavelu
Abstract:In this paper, solution of fuzzy differential equation under general differentiability is obtained by genetic programming (GP). The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.
Keywords: Fuzzy differential equation, Generalized differentiability, Genetic programming and H-difference.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2126
2502 Online Web Service based Solution for Urban Traffic Management
Authors: A. Ionita, A. Zafiu, C. Ghita
Abstract:In this article, we present a web server based solution for implementing a system for intelligent navigation. In this solution we use real time collected data and traffic history to establish the best route for navigation. This is a low cost solution that is easily to implement and extend. There is no need any infrastructure at road network level except only a device that collect data about traffic in key road crossing. The presented solution creates a strong base for traffic pursuit and offers an infrastructure for navigation applications.
Keywords: navigation, real time, route, traffic pursuit, webservice.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1476
2501 Using Memetic Algorithms for the Solution of Technical Problems
Authors: Ulrike Völlinger, Erik Lehmann, Rainer Stark
The intention of this paper is, to help the user of evolutionary algorithms to adapt them easier to their problem at hand. For a lot of problems in the technical field it is not necessary to reach an optimum solution, but to reach a good solution in time. In many cases the solution is undetermined or there doesn-t exist a method to determine the solution. For these cases an evolutionary algorithm can be useful. This paper intents to give the user rules of thumb with which it is easier to decide if the problem is suitable for an evolutionary algorithm and how to design them.
Keywords: Multi criteria optimization, Memetic algorithmsProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1300
2500 Group Invariant Solutions for Radial Jet Having Finite Fluid Velocity at Orifice
The group invariant solution for Prandtl-s boundary layer equations for an incompressible fluid governing the flow in radial free, wall and liquid jets having finite fluid velocity at the orifice are investigated. For each jet a symmetry is associated with the conserved vector that was used to derive the conserved quantity for the jet elsewhere. This symmetry is then used to construct the group invariant solution for the third-order partial differential equation for the stream function. The general form of the group invariant solution for radial jet flows is derived. The general form of group invariant solution and the general form of the similarity solution which was obtained elsewhere are the same.
Keywords: Two-dimensional jets, radial jets, group invariant solution.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1314
2499 Solution of Two Dimensional Quasi-Harmonic Equations with CA Approach
Authors: F. Rezaie Moghaddam, J. Amani, T. Rezaie Moghaddam
Abstract:Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.
Keywords: Heat conduction, Cellular automata, convergencerate, discrete system.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1659
2498 Simulink Approach to Solve Fuzzy Differential Equation under Generalized Differentiability
Authors: N. Kumaresan , J. Kavikumar, Kuru Ratnavelu
Abstract:In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.
Keywords: Fuzzy differential equation, Generalized differentiability, H-difference and Simulink.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2323
2497 Efficacy of Garlic and Chili Combination Solution on Cabbage Insect Pests and Crop Growth in Vietnam
Authors: Nguyen Minh Tuan, Bui Lan Anh, Bui Nu Hoang Anh
The study was conducted to evaluate the efficiency of Garlic and Chili combination solution on control of insect pests in cabbage crop. The solution was sprayed at different intervals after transplanting. The efficiency of Garlic and chili combination solution on cabbage insect pests was measured. Results revealed that Garlic and chili combination solution was the effectively reduced cabbage insect pests. On other hand, the spray solution not only reduced the number of days required for the cabbage growth but also greatly enhanced the leaf number, head diameter, head weight, and quality of cabbage. Garlic and chili combination solution have positive effects on pests reduction and improve growth, yield and quality of cabbage vegetable.
Keywords: Cabbage, Garlic, Chili, Diamondback moth, Cutworm, Flea Beetle, Quality.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6609
2496 An Approximate Solution of the Classical Van der Pol Oscillator Coupled Gyroscopically to a Linear Oscillator Using Parameter-Expansion Method
Authors: Mohammad Taghi Darvishi, Samad Kheybari
In this article, we are dealing with a model consisting of a classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. The major problem is analyzed. The regular dynamics of the system is considered using analytical methods. In this case, we provide an approximate solution for this system using parameter-expansion method. Also, we find approximate values for frequencies of the system. In parameter-expansion method the solution and unknown frequency of oscillation are expanded in a series by a bookkeeping parameter. By imposing the non-secularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation. One iteration step provides an approximate solution which is valid for the whole solution domain.
Keywords: Parameter-expansion method, classical Van der Pol oscillator.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1739
2495 Nylon Solution as Soil Stabilizer
Authors: G. M. Ayininuola, O. S. Oladeji
The research investigated the use of nylon solution to enhance the California bearing ratio (CBR) of soil. Used nylon sachet of potable water were dissolved in four separate solvents namely acetone, toluene, ethyl glycol and dual purpose kerosene (DPK). It was discovered that DPK has the highest nylon solubility of 29g/ml at 91oC. The nylon solution was used to stabilize poorly graded sandy soil. The result showed that at less or equal to 4% stabilization, the CBR value decreased from 25.3% to 15.85% and later appreciated to 67.78% at 16% stabilization. The initial decrease in CBR value of soil sample observed was as a result of inadequate nylon solution to coat soil particles for proper bonding.
Keywords: Nylon solution, Soil stabilization, Dual purpose kerosene, California bearing ratio.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3495
2494 Equivalence Class Subset Algorithm
Authors: Jeffrey L. Duffany
Abstract:The equivalence class subset algorithm is a powerful tool for solving a wide variety of constraint satisfaction problems and is based on the use of a decision function which has a very high but not perfect accuracy. Perfect accuracy is not required in the decision function as even a suboptimal solution contains valuable information that can be used to help find an optimal solution. In the hardest problems, the decision function can break down leading to a suboptimal solution where there are more equivalence classes than are necessary and which can be viewed as a mixture of good decision and bad decisions. By choosing a subset of the decisions made in reaching a suboptimal solution an iterative technique can lead to an optimal solution, using series of steadily improved suboptimal solutions. The goal is to reach an optimal solution as quickly as possible. Various techniques for choosing the decision subset are evaluated.
Keywords: np-complete, complexity, algorithm.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1252