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Issue No.01 - January/February (2012 vol.9)
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
ABSTRACT
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.
INDEX TERMS
Phylogeny, DNA, Bioinformatics, Computational biology, Computational complexity, Vegetation,satisfiability., ASP-complete, Betweenness, Quartet Challenge, phylogenetics, Quartet Compatibility
CITATION
M. L. Bonet, S. Linz, Katherine St. John, "The Complexity of Finding Multiple Solutions to Betweenness and Quartet Compatibility", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.9, no. 1, pp. 273-285, January/February 2012, doi:10.1109/TCBB.2011.108
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