k-colored Point-set Embeddability of Outerplanar Graphs

This paper addresses the problem of designing drawing algorithms that receive as input a planar graph G, a partitioning of the vertices of G into k different semantic categories V0, · · · , Vk−1, and k disjoint sets S0, · · · , Sk−1 of points in the plane with |Vi| = |Si| (i ∈ {0, · · · , k − 1}). The desired output is a planar drawing such that the vertices of Vi are mapped onto the points of Si and such that the curve complexity of the edges (i.e. the number of bends along each edge) is kept small. Particular attention is devoted to outerplanar graphs, for which lower and upper bounds on the number of bends in the drawings are established. Article Type Communicated by Submitted Revised Regular paper M. Kaufmann and D. Wagner December 2006 October 2007 Research partially supported by MIUR under Project “ALGO-NEXT(Algorithms for the Next Generation Internet and Web: Methodologies, Design and Experiments)”,