The breakpoint distance is one of the most straightforward genome comparison measures. Surprisingly, when it comes to define it precisely for multichromosomal genomes with both linear and circular chromosomes, there is more than one way to go about it. In this paper we study Single-Cut-or-Join (SCJ), a breakpoint-like rearrangement event for which we present linear and polynomial time algorithms that solve several genome rearrangement problems, such as median and halving. For the multichromosomal linear genome median problem, this is the first polynomial time algorithm described, since for other breakpoint distances this problem is NP-hard. These new results may be of value as a speedily computable, first approximation to distances or phytogenies based on more realistic rearrangement models.
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