Strongly rigid tensegrity graphs on the line

Tensegrity frameworks are defined on a set of points in R^d and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be strongly rigid in R^d if every generic realization in R^d as a tensegrity framework is infinitesimally rigid. In this note we show that it is NP-hard to test whether a given tensegrity graph is strongly rigid in R^1.