Algebraic rearrangement theory, as introduced by Meidanis and Dias, focuses on representing the order in which genes appear in chromosomes, and applies to circular chromosomes only. By shifting our attention to genome adjacencies, we are able to extend this theory to linear chromosomes in a very natural way, and extend the distance formula to the general multichromosomal case, with both linear and circular chromosomes. The resulting distance, which we call algebraic distance here, is very similiar to, but not quite the same as, DCJ distance. We present linear time algorithms to compute it and to sort genomes. We also show how to compute the algebraic distance from the adjacency graph. Some results on more general k-break distances are given, with algebraic distance being 2-break distance under our interpretation.
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