A polyhedral approach to sequence alignment problems

John D. Kececioglu, Hans Peter Lenhof, Kurt Mehlhorn, Petra Mutzel, Knut Reinert, Martin Vingron

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

We study two new problems in sequence alignment both from a practical and a theoretical view, using tools from combinatorial optimization to develop branch-and-cut algorithms. The generalized maximum trace formulation captures several forms of multiple sequence alignment problems in a common framework, among them the original formulation of maximum trace. The RNA sequence alignment problem captures the comparison of RNA molecules on the basis of their primary sequence and their secondary structure. Both problems have a characterization in terms of graphs which we reformulate in terms of integer linear programming. We then study the polytopes (or convex hulls of all feasible solutions) associated with the integer linear program for both problems. For each polytope we derive several classes of facet-defining inequalities and show that for some of these classes the corresponding separation problem can be solved in polynomial time. This leads to a polynomial-time algorithm for pairwise sequence alignment that is not based on dynamic programming. Moreover, for multiple sequences the branch-and-cut algorithms for both sequence alignment problems are able to solve to optimality instances that are beyond the range of present dynamic programming approaches.

Original languageEnglish (US)
Pages (from-to)143-186
Number of pages44
JournalDiscrete Applied Mathematics
Volume104
Issue number1-3
DOIs
StatePublished - Aug 15 2000

Keywords

  • Branch-and-cut
  • Combinatorial optimization
  • Computational biology
  • Multiple sequence alignment
  • RNA sequence alignment

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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