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This paper presents a simple linear algorithm for embedding (or drawing) a planar graph in the plane. The algorithm is based on the " vertex-addition " algorithm of Lempel, Even, and Cederbaum (" Theory of Graphs, " Intl. implementation of the testing algorithm using a PQ-tree. Compared with the known embedding algorithm of Hopcroft and Tarjan (J., this(More)
  • S. Abe
  • 1989
The Hopfield neural networks are well suited to solving large-scale optimization problems, but their convergence characteristics are not theoretically known. The author clarifies, by an eigenvalue analysis, conditions for converging to a vertex, a point on the edge, or an interior point of the hypercube. Taking the traveling salesman problem as an example,(More)
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