The objective of the assembly procedure is the minimization of the description length over all topologies of the form shown in figure 1, but there is no method for finding this minimum, short of exhaustive enumeration over all topologies, which is ruled out by practical considerations for all but the smallest S. We therefore adopt a greedy progressive method familiar from its use in multiple sequence alignment. At each stage, we find the pair of sequences (traces or partial assemblies) that provide the maximum saving in description length and assemble them, replacing the pair by the new assembly they have formed. The process continues until there are no remaining moves that lead to a description length reduction.