We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by O(27.55n ) = O(18...
Steinitz’s Theorem states that a graph is the 1-skeleton of a convex polyhedron if and only if it is 3-connected and planar. The polyhedron is called a geometric realization of ...
Dan Archdeacon, C. Paul Bonnington, Joanna A. Elli...
In this paper we deal with making drawings of clustered hierarchical graphs nicer. Given a planar graph G = (V, E) with an assignment of the vertices to horizontal layers, a plane ...
Given a planar graph G, we consider drawings of G in the plane where edges are represented by straight line segments (which possibly intersect). Such a drawing is specified by an i...
Mihyun Kang, Oleg Pikhurko, Alexander Ravsky, Math...
Greedy Routing is a class of routing algorithms in which the packets are forwarded in a manner that reduces the distance to the destination at every step. In an attempt to provide...