Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949124 | Computational Geometry | 2017 | 22 Pages |
Abstract
We study a problem motivated by rectilinear schematization of geographic maps. Given a biconnected plane graph G and an integer kâ¥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 OË(n10/7k1/7)-time algorithm to decide strict-orthogonal drawability, where OË(r) denotes O(rlogcâ¡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.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Md. Jawaherul Alam, Stephen G. Kobourov, Debajyoti Mondal,