TY - JOUR
T1 - Orthogonal layout with optimal face complexity
AU - Alam, Md Jawaherul
AU - Kobourov, Stephen G.
AU - Mondal, Debajyoti
N1 - Funding Information:
Work of the author is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC).
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - We study a problem motivated by rectilinear schematization of geographic maps. Given a biconnected plane graph G and an integer ≥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 =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 ˜(n10/7k1/7)-time algorithm to decide strict-orthogonal drawability, where O˜(r) denotes O(rlogcr), 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.
AB - We study a problem motivated by rectilinear schematization of geographic maps. Given a biconnected plane graph G and an integer ≥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 =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 ˜(n10/7k1/7)-time algorithm to decide strict-orthogonal drawability, where O˜(r) denotes O(rlogcr), 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.
KW - Face complexity
KW - Graph drawing
KW - Orthogonal drawing
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U2 - 10.1016/j.comgeo.2017.02.005
DO - 10.1016/j.comgeo.2017.02.005
M3 - Article
AN - SCOPUS:85014622190
VL - 63
SP - 40
EP - 52
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
SN - 0925-7721
ER -