  An important application of distance geometry to biochemistry studies the
embeddings of the vertices of a weighted graph in the three-dimensional
Euclidean space such that the edge weights are equal to the Euclidean distances
between corresponding point pairs. When the graph represents the backbone of a
protein, one can exploit the natural vertex order to show that the search space
for feasible embeddings is discrete. The corresponding decision problem can be
solved using a binary tree based search procedure which is exponential in the
worst case. We discuss assumptions that bound the search tree width to a
polynomial size.
