OPTIMAL COMPETITIVE HOPFIELD NETWORK WITH STOCHASTIC DYNAMICS FOR MAXIMUM CUT PROBLEM

2004 ◽  
Vol 14 (04) ◽  
pp. 257-265 ◽  
Author(s):  
JIAHAI WANG ◽  
ZHENG TANG ◽  
QIPING CAO ◽  
RONGLONG WANG
Keyword(s):  
Communication Networks ◽  
Stochastic Dynamics ◽  
Undirected Graph ◽  
Vlsi Circuits ◽  
Hopfield Network ◽  
Local Minima ◽  
Complete Problem ◽  
Maximum Cut ◽  
Np Complete ◽  
Better Than

In this paper, introducing stochastic dynamics into an optimal competitive Hopfield network model (OCHOM), we propose a new algorithm that permits temporary energy increases which helps the OCHOM escape from local minima. The goal of the maximum cut problem, which is an NP-complete problem, is to partition the node set of an undirected graph into two parts in order to maximize the cardinality of the set of edges cut by the partition. The problem has many important applications including the design of VLSI circuits and design of communication networks. Recently, Galán-Marín et al. proposed the OCHOM, which can guarantee convergence to a global/local minimum of the energy function, and performs better than the other competitive neural approaches. However, the OCHOM has no mechanism to escape from local minima. The proposed algorithm introduces stochastic dynamics which helps the OCHOM escape from local minima, and it is applied to the maximum cut problem. A number of instances have been simulated to verify the proposed algorithm.

scholarly journals Applying Neural Networks to Find the Minimum Cost Coverage of a Boolean Function

VLSI Design ◽  
1995 ◽  
Vol 3 (1) ◽  
pp. 13-19 ◽  
Author(s):  
Pong P. Chu
Keyword(s):  
Neural Network ◽  
Boolean Function ◽  
Input Data ◽  
Selection Process ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Hopfield Network ◽  
Neural Network Approach ◽  
Complete Problem ◽  
Np Complete

To find a minimal expression of a boolean function includes a step to select the minimum cost cover from a set of implicants. Since the selection process is an NP-complete problem, to find an optimal solution is impractical for large input data size. Neural network approach is used to solve this problem. We first formalize the problem, and then define an “energy function” and map it to a modified Hopfield network, which will automatically search for the minima. Simulation of simple examples shows the proposed neural network can obtain good solutions most of the time.

scholarly journals Genetic Algorithm for Independent Job Scheduling in Grid Computing

MENDEL ◽  
2017 ◽  
Vol 23 (1) ◽  
pp. 65-72 ◽  
Author(s):  
Muhanad Tahrir Younis ◽  
Shengxiang Yang
Keyword(s):  
Genetic Algorithm ◽  
Grid Computing ◽  
Job Scheduling ◽  
Computational Power ◽  
New Mutation ◽  
Complete Problem ◽  
Geographically Distributed ◽  
Np Complete ◽  
And Storage ◽  
Better Than

Grid computing refers to the infrastructure which connects geographically distributed computers ownedby various organizations allowing their resources, such as computational power and storage capabilities, to beshared, selected, and aggregated. Job scheduling is the problem of mapping a set of jobs to a set of resources.It is considered one of the main steps to e ciently utilise the maximum capabilities of grid computing systems.The problem under question has been highlighted as an NP-complete problem and hence meta-heuristic methodsrepresent good candidates to address it. In this paper, a genetic algorithm with a new mutation procedure tosolve the problem of independent job scheduling in grid computing is presented. A known static benchmark forthe problem is used to evaluate the proposed method in terms of minimizing the makespan by carrying out anumber of experiments. The obtained results show that the proposed algorithm performs better than some knownalgorithms taken from the literature.

AN ANNEALED CHAOTIC MAXIMUM NEURAL NETWORK FOR BIPARTITE SUBGRAPH PROBLEM

2004 ◽  
Vol 14 (02) ◽  
pp. 107-116 ◽  
Author(s):  
JIAHAI WANG ◽  
ZHENG TANG ◽  
RONGLONG WANG
Keyword(s):  
Neural Network ◽  
Parallel Algorithm ◽  
Chaotic Dynamics ◽  
Neural Model ◽  
Steepest Descent Method ◽  
Stable Equilibrium Point ◽  
Local Minima ◽  
Complete Problem ◽  
Bipartite Subgraph ◽  
Np Complete

In this paper, based on maximum neural network, we propose a new parallel algorithm that can help the maximum neural network escape from local minima by including a transient chaotic neurodynamics for bipartite subgraph problem. The goal of the bipartite subgraph problem, which is an NP–complete problem, is to remove the minimum number of edges in a given graph such that the remaining graph is a bipartite graph. Lee et al. presented a parallel algorithm using the maximum neural model (winner-take-all neuron model) for this NP–complete problem. The maximum neural model always guarantees a valid solution and greatly reduces the search space without a burden on the parameter-tuning. However, the model has a tendency to converge to a local minimum easily because it is based on the steepest descent method. By adding a negative self-feedback to the maximum neural network, we proposed a new parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm is then fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the maximum neural network and the chaotic neurodynamics. A large number of instances have been simulated to verify the proposed algorithm. The simulation results show that our algorithm finds the optimum or near-optimum solution for the bipartite subgraph problem superior to that of the best existing parallel algorithms.

COMPUTING THE RUPTURE DEGREE IN COMPOSITE GRAPHS

2010 ◽  
Vol 21 (03) ◽  
pp. 311-319 ◽  
Author(s):  
AYSUN AYTAC ◽  
ZEYNEP NIHAN ODABAS
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
The Other ◽  
Trade Off ◽  
Number Of Components ◽  
Np Complete ◽  
Work Done ◽  
Better Than

The rupture degree of an incomplete connected graph G is defined by [Formula: see text] where w(G - S) is the number of components of G - S and m(G - S) is the order of a largest component of G - S. For the complete graph Kn, rupture degree is defined as 1 - n. This parameter can be used to measure the vulnerability of a graph. Rupture degree can reflect the vulnerability of graphs better than or independent of the other parameters. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. Computing the rupture degree of a graph is NP-complete. In this paper, we give formulas for the rupture degree of composition of some special graphs and we consider the relationships between the rupture degree and other vulnerability parameters.

scholarly journals Statistical mechanics of an NP-complete problem: subset sum

2001 ◽  
Vol 34 (44) ◽  
pp. 9555-9567 ◽  
Author(s):  
Tomohiro Sasamoto ◽  
Taro Toyoizumi ◽  
Hidetoshi Nishimori
Keyword(s):  
Statistical Mechanics ◽  
Complete Problem ◽  
Subset Sum ◽  
Np Complete

scholarly journals Consecutive Colouring of Oriented Graphs

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Marta Borowiecka-Olszewska ◽  
Ewa Drgas-Burchardt ◽  
Nahid Yelene Javier-Nol ◽  
Rita Zuazua
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Bipartite Graphs ◽  
Complete Graphs ◽  
Oriented Graphs ◽  
Complete Problem ◽  
Np Complete

AbstractWe consider arc colourings of oriented graphs such that for each vertex the colours of all out-arcs incident with the vertex and the colours of all in-arcs incident with the vertex form intervals. We prove that the existence of such a colouring is an NP-complete problem. We give the solution of the problem for r-regular oriented graphs, transitive tournaments, oriented graphs with small maximum degree, oriented graphs with small order and some other classes of oriented graphs. We state the conjecture that for each graph there exists a consecutive colourable orientation and confirm the conjecture for complete graphs, 2-degenerate graphs, planar graphs with girth at least 8, and bipartite graphs with arboricity at most two that include all planar bipartite graphs. Additionally, we prove that the conjecture is true for all perfect consecutively colourable graphs and for all forbidden graphs for the class of perfect consecutively colourable graphs.

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