Embedding graphs in books: a layout problem with applications to VLSI design
SIAM Journal on Algebraic and Discrete Methods
Automatic graph drawing and readability of diagrams
IEEE Transactions on Systems, Man and Cybernetics
Crossing Minimization in Linear Embeddings of Graphs
IEEE Transactions on Computers
Neural network parallel computing
Neural network parallel computing
Graphs with E edges have pagenumber E O
Journal of Algorithms
An Efficient Multivalued Hopfield Network for the Traveling Salesman Problem
Neural Processing Letters
Algorithms for the fixed linear crossing number problem
Discrete Applied Mathematics
Computational Aspects of VLSI
IEEE Transactions on Computers
An N-parallel multivalued network: applications to the travelling salesman problem
IWANN'03 Proceedings of the Artificial and natural neural networks 7th international conference on Computational methods in neural modeling - Volume 1
Image compression by vector quantization with recurrent discrete networks
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part II
Graph partitioning via recurrent multivalued neural networks
IWANN'05 Proceedings of the 8th international conference on Artificial Neural Networks: computational Intelligence and Bioinspired Systems
A neural-network algorithm for a graph layout problem
IEEE Transactions on Neural Networks
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In this work, we propose the use of two neural models performing jointly in order to minimize the same energy function. This model is focused on obtaining good solutions for the two pages book crossing problem, although some others problems can be efficiently solved by the same model. The neural technique applied to this problem allows to reduce the energy function by changing outputs from both networks -outputs of first network representing location of nodes in the nodes line, while the outputs of the second one meaning the half-plane where the edges are drawn. Detailed description of the model is presented, and the technique to minimize an energy function is fully described. It has proved to be a very competitive and efficient algorithm, in terms of quality of solutions and computational time, when compared to the state-of-the-art methods. Some simulation results are presented in this paper, to show the comparative efficiency of the methods.