Efficiently Calculating Evolutionary Tree Measures Using SAT

  • Authors:
  • María Luisa Bonet;Katherine St. John

  • Affiliations:
  • Lenguajes y Sistemas Informáticos, Universidad Politécnica de Cataluña, Spain;Math & Computer Science Dept., Lehman College, City U., New York, USA

  • Venue:
  • SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
  • Year:
  • 2009

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Abstract

We develop techniques to calculate important measures in evolutionary biology by encoding to CNF formulas and using powerful SAT solvers. Comparing evolutionary trees is a necessary step in tree reconstruction algorithms, locating recombination and lateral gene transfer, and in analyzing and visualizing sets of trees. We focus on two popular comparison measures for trees: the hybridization number and the rooted subtree-prune-and-regraft (rSPR) distance. Both have recently been shown to be NP-hard, and efficient algorithms are needed to compute and approximate these measures. We encode these as a Boolean formula such that two trees have hybridization number k (or rSPR distance k ) if and only if the corresponding formula is satisfiable. We use state-of-the-art SAT solvers to determine if the formula encoding the measure has a satisfying assignment. Our encoding also provides a rich source of real-world SAT instances, and we include a comparison of several recent solvers (minisat, adaptg2wsat, novelty+p, Walksat, March KS and SATzilla).