Technical Report CS0552

Title: Two-Page Book Embedding of Trees Under Vertex-Neighborhood Constraints
Authors: S. Moran and Y. Wolfstahl
Abstract: We study the VLSI-related problem of embedding graphs in books. 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 from 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.

A black/white (blw) graph is a pair (G,U), where G is a graph and U in V is a subset of distinguished black vertices (the vertices of V-U are called white). A black/white (blw) book embedding of a blw graph (G ,U) is a book embedding of G, where the vertices of U are placed consecutively on the spine. The need for b/w embeddings may arise, for example, when the input ports of a multilayer VLSI chip are to be separated from the output ports.

In this paper we prove that every b/w tree admits a two-page b/w embedding. The proof takes the form of a linear time algorithm, which uses an extension of the unfolding technique inttoduced in [MW]. Combining this algorithm with the one in [MW] results in a linear time algorithm for optimal b/w embedding of trees.

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