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The Complexity of Finding Multiple Solutions to Betweenness and Quartet Compatibility

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3 Author(s)
Bonet, M.L. ; Dept. of Lenguajes y Sist. lnformaticos (LSI), Univ. Politec. de Catalunya (UPC), Barcelona, Spain ; Linz, S. ; St.John, K.

We show that two important problems that have applications in computational biology are ASP-complete, which implies that, given a solution to a problem, it is NP-complete to decide if another solution exists. We show first that a variation of BETWEENNESS, which is the underlying problem of questions related to radiation hybrid mapping, is ASP-complete. Subsequently, we use that result to show that QUARTET COMPATIBILITY, a fundamental problem in phylogenetics that asks whether a set of quartets can be represented by a parent tree, is also ASP-complete. The latter result shows that Steel's QUARTET CHALLENGE, which asks whether a solution to QUARTET COMPATIBILITY is unique, is coNP-complete.

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Computational Biology and Bioinformatics, IEEE/ACM Transactions on  (Volume:9 ,  Issue: 1 )