Testing the planar straight-line realizability of 2-trees with prescribed edge lengths

We study a classic problem introduced thirty years ago by Eades and Wormald. Let G=(V,E,λ) be a weighted planar graph, where λ:E→R+ is a length function. The Fixed Edge-Length Planar Realization problem (FEPR for short) asks whether there exists a planar straight-line realization of G, i.e., a planar straight-line drawing of G where the Euclidean length of each edge e∈E is λ(e).