New method to the solution of maximum clique problem: mean-field approximation algorithm and its experimentation

2002 ◽  
Author(s):  
Jijun Wu ◽  
T. Harada ◽  
T. Fukao
Keyword(s):  
Approximation Algorithm ◽  
Mean Field ◽  
Maximum Clique ◽  
Field Approximation ◽  
New Method ◽  
Mean Field Approximation ◽  
Maximum Clique Problem ◽  
Clique Problem

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

New Method for Latticeal Mean Field Models

1997 ◽  
Vol 11 (08) ◽  
pp. 339-345 ◽  
Author(s):  
Raluca S. Bundaru
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Free Energy ◽  
Mean Field ◽  
Field Approximation ◽  
New Method ◽  
Mean Field Approximation ◽  
Mean Field Models ◽  
The Mean

We develop a new method to find the free-energy for latticealsystems of classical spins in the mean-field approximation. The simplerecurrence relation which the Hamiltonian satisfies in this case, allows us to obtain the free-energy by solving an ordinary differential equation.

The Determination of the Magnetoelectric Coupling Coefficient in Ferroelectric–Ferromagnetic Composite Based on PZT–Ferrite

2013 ◽  
Vol 58 (4) ◽  
pp. 1401-1403 ◽  
Author(s):  
J.A. Bartkowska ◽  
R. Zachariasz ◽  
D. Bochenek ◽  
J. Ilczuk
Keyword(s):  
Dielectric Permittivity ◽  
Coupling Coefficient ◽  
Mean Field ◽  
Field Approximation ◽  
Theoretical Description ◽  
Magnetoelectric Coupling ◽  
Mean Field Approximation ◽  
Dielectric Measurements ◽  
Temperature Dependences ◽  
Multiferroic Composite

Abstract In the present work, the magnetoelectric coupling coefficient, from the temperature dependences of the dielectric permittivity for the multiferroic composite was determined. The research material was ferroelectric-ferromagnetic composite on the based PZT and ferrite. We investigated the temperature dependences of the dielectric permittivity (") for the different frequency of measurement’s field. From the dielectric measurements we determined the temperature of phase transition from ferroelectric to paraelectric phase. For the theoretical description of the temperature dependence of the dielectric constant, the Hamiltonian of Alcantara, Gehring and Janssen was used. To investigate the dielectric properties of the multiferroic composite this Hamiltonian was expressed under the mean-field approximation. Based on dielectric measurements and theoretical considerations, the values of the magnetoelectric coupling coefficient were specified.

scholarly journals Hexagonal-Shaped Spin Crossover Nanoparticles Studied by Ising-Like Model Solved by Local Mean Field Approximation

2021 ◽  
Vol 7 (5) ◽  
pp. 69
Author(s):  
Catherine Cazelles ◽  
Jorge Linares ◽  
Mamadou Ndiaye ◽  
Pierre-Richard Dahoo ◽  
Kamel Boukheddaden
Keyword(s):  
Spin Crossover ◽  
Hexagonal Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ligand Field ◽  
Order And Disorder ◽  
The Matrix ◽  
Local Mean ◽  
Parameter Values

The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short- and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (TO.D.) of internal coupling origin and the ligand field-dependent equilibrium temperatures (Teq) of external origin.

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