Straight-Line Grid Drawings of Label-Constrained Outerplanar Graphs with O(n log n) Area

A straight-line grid drawing of a planar graph G is a drawing of G on an integer grid such that each vertex is drawn as a grid point and each edge is drawn as a straight-line segment without edge crossings. Any outerplanar graph of n vertices with maximum degree d has a straight-line grid drawing with area O(dn log n). In this paper, we introduce a subclass of outerplanar graphs, which we call label-constrained outerplanar graphs, that admits straight-line grid drawings with O(n log n) area. We give a linear-time algorithm to find such a drawing. We also give a linear-time algorithm for the recognition of label-constrained outerplanar graphs. Submitted: May 2009 Reviewed: September 2009 Revised: July 2010 Accepted: October 2010 Final: December 2010 Published: July 2011 Article type: Regular paper Communicated by: S. Das and R. Uehara E-mail addresses: [email protected] (Md. Rezaul Karim) [email protected] (Md. Jawaherul Alam) [email protected] (Md. Saidur Rahman) 438 Karim et al. Drawings of Label-Constrained Outerplanar Graphs