  We discuss whether it is possible to reconstruct a metric by its
unparameterized geodesics, and how to do it effectively. We explain why this
problem is interesting for general relativity. We show how to understand
whether all curves from a sufficiently big family are umparameterized geodesics
of a certain affine connection, and how to reconstruct algorithmically a
generic 4-dimensional metric by its unparameterized geodesics. The algorithm
works most effectively if the metric is Ricci-flat. We also prove that almost
every metric does not allow nontrivial geodesic equivalence, and construct all
pairs of 4-dimensional geodesically equivalent metrics of Lorenz signature.
