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arXiv · 1708.06730

Upward Partitioned Book Embeddings

Hugo A. Akitaya·Erik D. Demaine·Adam Hesterberg·Quanquan C. Liu
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Abstract

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 $k\ge 3$, and for $k\ge 4$ 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.

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BibTeXRIS

Hugo A. Akitaya, Erik D. Demaine, Adam Hesterberg, Quanquan C. Liu. 2017-08-22. Upward Partitioned Book Embeddings. https://arxiv.org/abs/1708.06730

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