  The problem of reconstructing a sequence of independent and identically
distributed symbols from a set of equal size, consecutive, fragments, as well
as a dependent reference sequence, is considered. First, in the regime in which
the fragments are relatively long, and typically no fragment appears more than
once, the scaling of the failure probability of maximum likelihood
reconstruction algorithm is exactly determined for perfect reconstruction and
bounded for partial reconstruction. Second, the regime in which the fragments
are relatively short and repeating fragments abound is characterized. A
trade-off is stated between the fraction of fragments that cannot be adequately
reconstructed vs. the distortion level allowed for the reconstruction of each
fragment, while still allowing vanishing failure probability
