Constrained Point-Set Embeddability of Planar Graphs [chapter]

Emilio Di Giacomo, Walter Didimo, Giuseppe Liotta, Henk Meijer, Stephen Wismath
2009 Lecture Notes in Computer Science  
This paper starts the investigation of a constrained version of the point-set embeddability problem. Let G = (V, E) be a planar graph with n vertices, G = (V , E ) a subgraph of G, and S a set of n distinct points in the plane. We study the problem of computing a point-set embedding of G on S subject to the constraint that G is drawn with straight-line edges. Different drawing algorithms are presented that guarantee small curve complexity of the resulting drawing, i.e. a small number of bends
more » ... r edge. It is proved that: (i) If G is an outerplanar graph and S is any set of points in convex position, a point-set embedding of G on S can be computed such that the edges of E \ E have at most 4 bends each. (ii) If S is any set of points in general position and G is a face of G or if it is a simple path, the curve complexity of the edges of E \ E is at most 8. (iii) If S is in general position and G is a set of k disjoint paths, the curve complexity of the edges of E \ E is O(2 k ).
doi:10.1007/978-3-642-00219-9_35 fatcat:rpmcokecjrauvf7sdsrndkwv54