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A near-optimum parallel planarization algorithm.

Y Takefuji, K C Lee

    Science (New York, N.Y.)
    |September 15, 1989
    PubMed
    Summary
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    This study introduces a near-optimum parallel planarization algorithm using neural networks to embed graphs on a plane. The algorithm efficiently generates planar subgraphs and embeds them in constant time, aiding complex circuit designs.

    Area of Science:

    • Computer Science
    • Graph Theory
    • Artificial Intelligence

    Background:

    • Graph planarization is crucial for electronic design automation.
    • Existing algorithms can be computationally intensive.
    • Efficient embedding of planar graphs is a persistent challenge.

    Purpose of the Study:

    • To present a near-optimum parallel planarization algorithm.
    • To develop a neural network-based approach for graph embedding.
    • To achieve constant time complexity for planar subgraph generation and embedding.

    Main Methods:

    • Utilized an N x N neural network array, where N represents the number of vertices.
    • Developed a parallel algorithm for graph planarization.
    • Focused on generating near-maximal planar subgraphs.

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    Main Results:

    • The algorithm achieves near-optimum results for planarization.
    • The system successfully embeds planar subgraphs on a single plane.
    • Demonstrated a time complexity of O(1) for the embedding process.

    Conclusions:

    • The proposed neural network-based algorithm offers an efficient solution for graph planarization.
    • The O(1) time complexity makes it suitable for real-time applications.
    • Applicable to multi-layer problems like printed circuit board design and VLSI routing.