Upward Partitioned Book Embeddings
نویسندگان
چکیده
We analyze a directed variation of the book embedding problem when the page partition is prespecified and the nodes on the spine must be in topological order (upward book embedding). Given a directed acyclic graph and a partition of its edges into k pages, can we linearly order the vertices such that the drawing is upward (a topological sort) and each page avoids crossings? We prove that the problem is NP-complete for k ≥ 3, and for k ≥ 4 even in the special case when each page is a matching. By contrast, the problem can be solved in linear time for k = 2 pages when pages are restricted to matchings. The problem comes from Jack Edmonds (1997), motivated as a generalization of the map folding problem from computational origami.
منابع مشابه
Upward Topological Book Embeddings of DAGs
Let G be a directed acyclic graph. An upward (k, h)topological book embedding of G is an upward book embedding on k pages of a subdivision of G where every edge is replaced by a path having at most h+2 vertices. In this extended abstract it is shown that every DAG with n vertices admits an upward (d + 1, 2dlogd ne − 1)-topological book embedding, where d is any integer such that d ≥ 2. The resu...
متن کاملComputing Upward Topological Book Embeddings of Upward Planar Digraphs
This paper studies the problem of computing an upward topological book embedding of an upward planar digraph G, i.e. a topological book embedding of G where all edges are monotonically increasing in the upward direction. Besides having its own inherent interest in the theory of upward book embeddability, the question has applications to well studied research topics of computational geometry and...
متن کاملSpine Crossing Minimization in Upward Topological Book Embeddings
An upward topological book embedding of a planar st-digraph G is an upward planar drawing of G such that its vertices are aligned along the vertical line, called the spine, and each edge is represented as a simple Jordan curve which is divided by the intersections with the spine (spine crossings) into segments such that any two consecutive segments are located at opposite sides of the spine. Wh...
متن کاملOptimal Acyclic Hamiltonian Path Completion for Outerplanar Triangulated st-Digraphs (with Application to Upward Topological Book Embeddings)
Given an embedded planar acyclic digraph G, we define the problem of"acyclic hamiltonian path completion with crossing minimization (Acyclic-HPCCM)"to be the problem of determining an hamiltonian path completion set of edges such that, when these edges are embedded on G, they create the smallest possible number of edge crossings and turn G to a hamiltonian digraph. Our results include: --We pro...
متن کاملUpward Geometric Graph Embeddings into Point Sets
We study the problem of characterizing the directed graphs with an upward straightline embedding into every point set in general or in convex position. We solve two questions posed by Binucci et al. [Computational Geometry: Theory and Applications, 2010 ]. Namely, we prove that the classes of directed graphs with an upward straightline embedding into every point set in convex position and with ...
متن کامل