NDLI: Vertex Types in Book-Embeddings

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Vertex Types in Book-Embeddings

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Rosenberg, Arnold L. Knott, Judson D. Buss, Jonathan F.
Copyright Year	1989
Abstract	A new measure of the complexity of a book-embedding of a simple undirected graph, the number of vertex types in the embedding, is studied. The type of a vertex $v $ in a p-page book-embedding is the $p \times 2$ matrix of nonnegative integers \[ \tau (v ) = \begin{pmatrix} L_1 & & R_1 \\ L_2 & & R_2 \\ & \vdots & \\ L_P & & {R_P } \end{pmatrix}, \] where $L_i $; (respectively, $R_i $) is the number of edges incident to $v $ that connect on page i to vertices lying to the left (respectively, to the right) of $v $. The number of types in a book-embedding relates to the amount of logic necessary to realize fault-tolerant arrays of processors using one specific design methodology. Three sorts of issues regarding vertex types in book-embeddings are studied. A number of techniques for bounding the type-numbers of a variety of graphs are developed; the relationships between typenumber and other graph properties, such as book thickness, are investigated; and the problem of minimizing the typenumber of a graph is considered. Finding that problem to be NP-complete, the problem of finding a (cyclic) rotation of a given book-embedding that minimizes the number of vertex types is studied.
Starting Page	156
Ending Page	175
Page Count	20
File Format	PDF
ISSN	08954801
DOI	10.1137/0402015
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	2
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-08
Access Restriction	Subscribed
Subject Keyword	Planar graphs; geometric and topological aspects of graph theory fault-tolerance NP-completeness graph embedding VLSI design Graph theory trees outerplanar graphs
Content Type	Text
Resource Type	Article
Subject	Mathematics

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