Polynomial cases of the Discretizable Molecular Distance Geometry   Problem
  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. 
Leo Liberti, Carlile Lavor, Benoit Masson, Antonio Mucherino
cs.CG cs.CE cs.DS q-bio.QM