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We define a “threaded blockset,” which is a novel generalization of the classic notion of a multiple alignment. A new computer program called TBA (for “threaded blockset aligner”) builds a threaded blockset under the assumption that all matching segments occur in the same order and orientation in the given sequences; inversions and duplications are not addressed. TBA is designed to be appropriate for aligning many, but by no means all, megabase-sized regions of multiple mammalian genomes. The output of TBA can be projected onto any genome chosen as a reference, thus guaranteeing that different projections present consistent predictions of which genomic positions are orthologous. This capability is illustrated using a new visualization tool to view TBA-generated alignments of vertebrate Hox clusters from both the mammalian and fish perspectives. Experimental evaluation of alignment quality, using a …