A near-optimum parallel planarization algorithm is presented. The planarization algorithm, which is designed to embed a graph on a plane, uses a large number of simple processing elements called neurons. The proposed system, composed of an N×N neural network array (where N is the number of vertices), not only generates a near-maximal planar subgraph from a nonplanar graph or a planar graph but also embeds the subgraph on a single plane within 0(1) time. The algorithm can be used in multiple-layer problems such as designing printed circuit boards and routing very-large-scale integration circuits.
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