Article ID Journal Published Year Pages File Type
4949124 Computational Geometry 2017 22 Pages PDF
Abstract
We study a problem motivated by rectilinear schematization of geographic maps. Given a biconnected plane graph G and an integer k≥0, does G have a strict-orthogonal drawing (i.e., an orthogonal drawing without edge bends) with at most k reflex angles per face? For k=0, the problem is equivalent to realizing each face as a rectangle. We prove that the strict-orthogonal drawability problem for arbitrary reflex complexity k can be reduced to a graph matching or a network flow problem. Consequently, we obtain an O˜(n10/7k1/7)-time algorithm to decide strict-orthogonal drawability, where O˜(r) denotes O(rlogc⁡r), for some constant c. In contrast, if the embedding is not fixed, we prove that it is NP-complete to decide whether a planar graph admits a strict-orthogonal drawing with reflex face complexity 4.
Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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