Upward Partitioned Book Embeddings
Author(s)Akitaya, Hugo A.; Demaine, Erik D; Hesterberg, Adam Classen; Liu, Quanquan C.
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
International Symposium on Graph Drawing and Network Visualization
Springer International Publishing
Akitaya, Hugo A. et al. "Upward Partitioned Book Embeddings." International Symposium on Graph Drawing and Network Visualization, September 2018, Barcelona, Spain, Springer International Publishing, January 2018. © 2018 Springer International Publishing AG