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

Abstract

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(dnlog 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(nlog 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.