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.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

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 -