Abstract
A Hamming space Λ n consists of all sequences of length n over an alphabet Λ and is endowed with the Hamming distance. In particular, any set of aligned DNA sequences of fixed length constitutes a subspace of a Hamming space with respect to mismatch distance. The quasi-median operation returns for any three sequences u , v , w the sequence which in each coordinate attains either the majority coordinate from u , v , w or else (in the case of a tie) the coordinate of the first entry, u ; for a subset of Λ n the iterative application of this operation stabilizes in its quasi-median hull. We show that for every finite tree interconnecting a given subset X of Λ n there exists a shortest realization within Λ n for which all interior nodes belong to the quasi-median hull of X . Hence the quasi-median hull serves as a Steiner hull for the Steiner problem in Hamming space.
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