  We initiate the theoretical study of directory reconciliation, a
generalization of document exchange, in which Alice and Bob each have different
versions of a set of documents that they wish to synchronize. This problem is
designed to capture the setting of synchronizing different versions of file
directories, while allowing for changes of file names and locations without
significant expense. We present protocols for efficiently solving directory
reconciliation based on a reduction to document exchange under edit distance
with block moves, as well as protocols combining techniques for reconciling
sets of sets with document exchange protocols. Along the way, we develop a new
protocol for document exchange under edit distance with block moves inspired by
noisy binary search in graphs, which uses only $O(k \log n)$ bits of
communication at the expense of $O(k \log n)$ rounds of communication.
