Two-Page Book Embedding of Trees under Vertex-Neighborhood Constraints

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 ~ along the spine of the book, and (2) an assignment of each ee E to a page of the book, so that edges assigned to the same page do nOt int&sect. 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~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 p<rts 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. T ec hn io n C om pu te r Sc ie nc e D ep ar tm en t T eh ni ca l R ep or t C S0 55 2 19 89