Reconciliation Puzzles

We consider the problem of exchanging two similar strings held by different hosts with a minimum amount of communication. We reduce the problem of string reconciliation to a problem of multi-set reconciliation, for which nearly optimal solutions exist. Our approach involves transforming a string into a multi-set of substrings, which are reconciled efficiently and then put back together on a remote host using recent graph-theoretic results. We present an analysis of our algorithm to show that its communication complexity compares favorably to an existing method for string reconciliation. A version of this article will appear as: V. Chauhan and A. Trachtenberg, “Reconciliation puzzles”, IEEE Globecom 2004, Dallas, TX.