Orthogonal layout with optimal face complexity

Md Jawaherul Alam, Stephen G. Kobourov, Debajyoti Mondal

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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(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.

Original languageEnglish (US)
Pages (from-to)40-52
Number of pages13
JournalComputational Geometry: Theory and Applications
StatePublished - Jun 1 2017


  • Face complexity
  • Graph drawing
  • Orthogonal drawing

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


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