Comparison of large, unfinished genomic sequences requires fast methods that are robust to misordering, misorientation, and duplications. A number of fast methods exist that can compute local similarities between such sequences, from which an optimal one-to-one correspondence might be desired. However, existing methods for computing such a correspondence are either too costly to run or are inappropriate for unfinished sequence. We propose an efficient method for refining a set of segment matches such that the resulting segments are of maximal size without non-identity overlaps. This resolved set of segments can be used in various ways to compute a similarity measure between any two large sequences, and hence can be used in alignment, matching, or tree construction algorithms for two or more sequences.