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Issue No. 01 - January/February (2012 vol. 9)
ISSN: 1545-5963
pp: 273-285
M. L. Bonet , Dept. of Lenguajes y Sist. lnformaticos (LSI), Univ. Politec. de Catalunya (UPC), Barcelona, Spain
S. Linz , Center for Bioinf. (ZBIT), Univ. of Tubingen, Tubingen, Germany
Katherine St. John , Dept. of Math. & Comput. Sci., City Univ. of New York, Boulevard West, NY, USA
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.
Phylogeny, DNA, Bioinformatics, Computational biology, Computational complexity, Vegetation

M. L. Bonet, S. Linz and K. St. John, "The Complexity of Finding Multiple Solutions to Betweenness and Quartet Compatibility," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 9, no. 1, pp. 273-285, 2011.
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