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SIAM Journal on Discrete Mathematics
Article . 1990 . Peer-reviewed
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Article . 2002 . Peer-reviewed
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One-Page Book Embedding under Vertex-Neighborhood Constraints

One-page book embedding under vertex-neighborhood constraints
Authors: Moran, Shlomo; Wolfstahl, Yaron;

One-Page Book Embedding under Vertex-Neighborhood Constraints

Abstract

Summary: The VLSI-related problem of embedding graphs in books is studied. A book embedding of a graph \(G=(V,E)\) consists of two parts, namely, (1) an ordering of \(V\) along the spine of the book, and (2) an assignment of each \(e\in E\) to a page of the book, so that edges assigned to the same page do not intersect. In devising an embedding, one seeks to minimize the number of pages used. This paper addresses a generalization of the book embedding problem, called the black/white \((b/w)\) book embedding problem, where a vertex- neighborhood constraint is imposed on the ordering of the vertices. A \(b/w\) graph is a pair \((G,U)\), where \(G=(V,E)\) is a graph and \(U\subseteq V\) is a set of distinguished black vertices (the vertices in \(V-U\) are called white). A \(b/w\) book embedding of \((G,U)\) is a book embedding of \(G\), where the black vertices are arranged consecutively along the spine. Given a \(b/w\) graph \((G,U)\), the \(b/w\) book embedding problem is that of finding a \(b/w\) book embedding of \((U,G)\), such that the number of pages is minimized. The need for \(b/w\) embeddings may arise, for example, in applications where the input ports of a VLSI chip are to be separated from the output ports. The main result is a characterization of the \(b/w\) graphs that admit a one-page \(b/w\) embedding. The characterization is given in terms of a set of forbidden \(b/w\) subgraphs, the absence of which is necessary and sufficient for one-page \(b/w\) embedding. For a \(b/w\) graph with none of these forbidden subgraphs, a one-page \(b/w\) embedding is constructible in linear time. The construction utilizes a technique called \(b/w\) unfolding, which is a feature of independent interest.

Keywords

outerplanar graphs, Eulerian and Hamiltonian graphs, algorithm, book embedding, Planar graphs; geometric and topological aspects of graph theory, Hardware implementations of nonnumerical algorithms (VLSI algorithms, etc.), Applications of graph theory to circuits and networks

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Average
Top 10%
Average
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