Computational Balloon Twisting: The Theory of Balloon Polyhedra

This paper builds a general mathematical and algorithmic theory for balloon-twisting structures, from balloon animals to balloon polyhedra, by modeling their underlying graphs (edge skeleta). In particular, we give algorithms to find the fewest balloons that can make exactly a desired graph or, using fewer balloons but allowing repeated traversal or shortcuts, the minimum total length needed by a given number of balloons. In contrast, we show NP-completeness of determining whether such an optimal construction is possible with balloons of equal length. What if Euler were a clown? (a) Classic dog (one balloon). (b) Octahedron (one balloon). Figure 1: Two one-balloon constructions and their associated graphs.

• Type: Conference
• Year: 2008
• Where: CCCG
• Authors: Erik D. Demaine, Martin L. Demaine, Vi Hart
• Keywords: Balloon Polyhedra, CCCG 2008, Computational Geometry, Fewest Balloons, Minimum Total Length