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Vertex Types in Book-Embeddings
SIAM Journal on Discrete Mathematics, 1989A 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 ...
Arnold L. Rosenberg +2 more
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Structured Word Embedding for Low Memory Neural Network Language Model
Interspeech, 2018Neural network language model (NN LM), such as long short term memory (LSTM) LM, has been increasingly popular due to its promising performance. However, the model size of an uncompressed NN LM is still too large to be used in embedded or portable ...
Kaiyu Shi, Kai Yu
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Book Embeddings of Nonplanar Graphs with Small Faces in Few Pages
International Symposium on Computational Geometry, 2020An embedding of a graph in a book, called book embedding, consists of a linear ordering of its vertices along the spine of the book and an assignment of its edges to the pages of the book, so that no two edges on the same page cross.
M. Bekos +5 more
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Book embeddings and crossing numbers
1995The paper introduces the book crossing number problem which can be viewed as a variant of the well-known plane and surface crossing number problem or as a generalization of the book embedding problem. The book crossing number of a graph G is defined as the minimum number of edge crossings when the vertices of G are placed on the spine of a k-page book ...
Imrich Vrto +3 more
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Embedding graphs in books: a survey
IEE Proceedings E Computers and Digital Techniques, 1992Embedding a graph in a book is an arrangement of vertices in a line along the spine of the book and edges on the pages in such a way that edges residing on the same page do not cross. Each graph has many different embeddings in books. The embedding with the minimum number of pages is optimum.
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A Designer Embedded Book Space Experiment
2021The relationship between books and their readers are intimacy and personal. The texts are firsthand resources for readers experience personal journey while reading, and their own unparalleled inspiration. The reflection after reading could be represented in diverse fashions, most of them were written using words as reviews.
Tao-Tao Yu, Teng Wen Chang
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Book embedding of the k-ary hypercube
2008 First International Conference on the Applications of Digital Information and Web Technologies (ICADIWT), 2008Graph embeddings play an important role in interconnection network and VLSI design. Determining the number of layers required to build a VLSI chip is just one of the many areas in which graph embeddings are used. A type of embedding that is helpful in determining the number of layers is a book embedding.
D. Hoelzeman, Said Bettayeb
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Embedding iterated line digraphs in books
Networks, 2002AbstractIn this paper, we present an upper bound on the pagenumber of an iterated line digraph Lk(G) of a digraph G. Our bound depends only on the digraph G and is independent of the number of iterations k. In particular, it is proved that the pagenumber of Lk(G) does not increase with the number of iterations k.
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Embedding Outerplanar Graphs in Small Books
SIAM Journal on Algebraic Discrete Methods, 1987A book consists of a number of half-planes (pages) sharing a common boundary line (the spine). A book embedding of a graph embeds the vertices on the spine and each edge in some page so that each page contains a plane subgraph. The width of a page is the maximum number of edges that intersect any half-line perpendicular to the spine in the page.
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A survey on book-embedding of planar graphs
Frontiers of Mathematics in China, 2022Xiaxia Guan +3 more
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