A computational challenge raised by chromosome conformation capture (3C) experiments is to reconstruct spatial distances and three-dimensional genome structures from observed contacts between genomic loci. We propose a two-step algorithm, ShRec3D, and assess its accuracy using both in silico data and human genome-wide 3C (Hi-C) data. This algorithm avoids convergence issues, accommodates sparse and noisy contact maps, and is orders of magnitude faster than existing methods.