Upward Partitioned Book Embeddings

08/22/2017

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by   Hugo A. Akitaya, et al.

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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.