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An 0(mn) Algorithm for Embedding Graphs into a 3-Page Book
Miki SHIMABARA MIYAUCHI
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1994/03/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on the 6th Karuizawa Workshop on Circuits and Systems)
Category: Graphs, Networks and Matroids
graphs, algorithms, data structures and computational complexity, VLSI design technology,
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This paper studies the problem of embedding a graph into a book with nodes on a line along the spine of the book and edges on the pages in such a way that no edge crosses another. Atneosen as well as Bernhart and Kainen has shown that every graph can be embedded into a 3-page book when each edge can be embedded in more than one page. The time complexity of Bernhart and Kainen's method is Ω(ν(G)), where ν(G) is the crossing number of a graph G. A new 0(mn) algorithm is derived in this paper for embedding a graph G=(V, E), where m=│E│ and n= │V│ . The number of points at which edges cross over the spine in embedding a complete graph into a 3-page book is also investigated.