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- W151167536 abstract "We investigate the problem of embedding graphs in books. A book is some number of half-planes (the pages of the book), which share a common line as boundary (the spine of the book). A book embedding of a graph embeds the vertices on the spine in some order and embeds each edge in some page so that in each page no two edges intersect. The pagenumber of a graph is the number of pages in a minimum-page embedding of the graph. The pagewidth of a book embedding is the maximum cutwidth of the embedding in any page. A practical application is in the realization of a fault-tolerant array of VLSI processors.Our results are efficient algorithms for embedding certain classes of planar graphs in books of small pagenumber or small pagewidth.The first result is a linear time algorithm that embeds any planar graph in a book of seven pages. This establishes the smallest upper bound known for the pagenumber of the class of planar graphs. The algorithm uses three main ideas. The first is to level the planar graph. The second is to extend a cycle at one level to the next level by doing micro-surgery. The third is to nest the embedding of successive levels to obtain finite pagenumber.The second result is a linear time algorithm that embeds any trivalent planar graph in a book of two pages. The algorithm edge-augments the graph to make it hamiltonian while keeping it planar.The third result is an O(n log n) time algorithm for embedding any outerplanar graph with small pagewidth. Our algorithm embeds any d-valent outerplanar graph in a two-page book with O(d log n) pagewidth. This result is optimal in pagewidth to within a constant factor. The significance for VLSI design is that any outerplanar graph can be implemented in small area in a fault-tolerant fashion." @default.
- W151167536 created "2016-06-24" @default.
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- W151167536 date "1985-01-01" @default.
- W151167536 modified "2023-09-23" @default.
- W151167536 title "Algorithms for embedding graphs in books (planar, vlsi, fault-tolerant, hamiltonian cycle, trivalent)" @default.
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