The wobbly logic engine: Proving hardness of non-rigid geometric graph representation problems

The logic engine technique has been used in the past to establish the NP-hardness of a number of graph representations. The original technique can only be applied in those situations in which subgraphs exist for which the only possible layouts are rigid. In this paper we introduce an extension called the wobbly logic engine which can be used to prove the NP-hardness of several graph representations for which no such rigid layouts exist, representations by visibility and intersection in particular. We illustrate the method by using the wobbly technique to show the NP-hardness of deciding whether a graph has a nondegenerate z-axis parallel visibility representation (ZPR) by unit squares.