Algorithms to find optimal alignments among strings, or to find a
parsimonious summary of a collection of strings, are well studied in a
variety of contexts, addressing a wide range of interesting
applications. In this paper, we consider \emph{chain letters,} which
contain a growing sequence of signatories added as the letter
propagates. The unusual constellation of features exhibited by chain
letters (one-ended growth, divergence, and mutation) make their
propagation, and thus the corresponding reconstruction problem, both
distinctive and rich. Here, inspired by these chain letters, we
formally define the problem of computing an optimal summary of a set
of diverging string sequences. From a collection of these sequences
of names, with each sequence noisily corresponding to a branch of the
unknown tree $T$ representing the letter's true dissemination, can we
efficiently and accurately reconstruct a tree $T' \approx T$? In this
paper, we give efficient exact algorithms for this summarization
problem when the number of sequences is small; for larger sets of
sequences, we prove hardness and provide an efficient heuristic
algorithm. We evaluate this heuristic on synthetic data sets chosen
to emulate real chain letters, showing that our algorithm is
competitive with or better than previous approaches, and that it also
comes close to finding the true trees in these synthetic datasets.