Orthogonal-Ordering Constraints are Tough

We show that rectilinear graph drawing, the core problem of bendminimum orthogonal graph drawing, and uniform edge-length drawing, the core problem of force-directed placement, are NP-hard even for embedded paths if subjected to orthogonal-ordering constraints. Submitted: June 2010 Reviewed: April 2011 Revised: September 2012 Accepted: November 2012 Final: December 2012 Published: January 2013 Article type: Concise paper Communicated by: G. Di Battista A preliminary version of this paper appeared as U. Brandes and B. Pampel: On the hardness of orthogonal-order preserving graph drawing, in Proc. Intl. Symp. Graph Drawing (GD ’08), Springer Lecture Notes in Computer Science vol. 5417, pp. 266–277, 2009. We are grateful to two anonymous reviewers whose comments helped to improve the exposition. E-mail addresses: [email protected] (Ulrik Brandes) [email protected] (Barbara Pampel) 2 Brandes and Pampel Orthogonal-Ordering Constraints are Tough