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Book Embeddings and Point-Set Embeddings of Series-Parallel Digraphs

Di Giacomo, Emilio and Didimo, Walter and Liotta, Giuseppe and Wismath, Stephen (2002) Book Embeddings and Point-Set Embeddings of Series-Parallel Digraphs. [Conference Paper]

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Abstract

An optimal O(n)-time algorithm to compute an upward two-page book embedding of a series-parallel digraph with n vertices is presented. A previous algorithm of Alzohairi and Rival [1] runs in O(n³) time and assumes that the input series-parallel digraph does not have transitive edges. One consequence of our result is that series-parallel (undirected) graphs are necessarily sub-hamiltonian. This extends a previous resu lt by Chung, Leighton, and Rosenberg [5] who proved sub-hamiltonicity for a subset of planar series-parallel graphs. Also, this paper investigates the problem of mapping planar digraphs onto a given set of points in the plane, so that the edges are drawn upward planar. This problem is called the upward point-set embedding problem. The equivalence between the problem of computing an upward two-page book embedding and an upward point-set embedding with at most one bend per edge on any given set of points is proved. An O(n log n)-time algorithm for computing an upward point-set embedding with at most one bend per edge on any given set of points for planar series-parallel digraphs is presented.

Item Type:Conference Paper
Classifications:P Styles > P.840 Upward
M Methods > M.999 Others
G Algorithms and Complexity > G.490 Embeddings
G Algorithms and Complexity > G.999 Others
ID Code:299
Deposited By:Martinez Leon, Victoria
Deposited On:01 Dec 2004
Last Modified:18 Sep 2008 13:08
Alternative Locations:http://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=2528&spage=162

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References

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