In this paper we deal with the problem of computing upward two-page book embeddings of Two Terminal Series–Parallel (TTSP) digraphs, which are a subclass of series–parallel digraphs. An optimal O(n) time and space algorithm to compute an upward two-page book embedding of a TTSP-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. An application of this result to a computational geometry problem is also discussed. More precisely, upward two-page book embeddings are used to deal with the upward point-set embeddability problem, i.e., the problem of mapping planar digraphs onto a given set of points in the plane so that all edges are monotonically increasing in a common direction. The equivalence between upward two-page book embeddability and upward point-set embeddability 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 for TTSP-digraphs is presented.
Book Embeddability of Series-Parallel Digraphs
DI GIACOMO, Emilio;DIDIMO, WALTER;LIOTTA, Giuseppe;
2006
Abstract
In this paper we deal with the problem of computing upward two-page book embeddings of Two Terminal Series–Parallel (TTSP) digraphs, which are a subclass of series–parallel digraphs. An optimal O(n) time and space algorithm to compute an upward two-page book embedding of a TTSP-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. An application of this result to a computational geometry problem is also discussed. More precisely, upward two-page book embeddings are used to deal with the upward point-set embeddability problem, i.e., the problem of mapping planar digraphs onto a given set of points in the plane so that all edges are monotonically increasing in a common direction. The equivalence between upward two-page book embeddability and upward point-set embeddability 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 for TTSP-digraphs is presented.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
