Abstract
© 2004-2012 IEEE.Parsimony haplotyping is the problem of finding a set of haplotypes of minimum cardinality that explains a given set of genotypes, where a genotype is explained by two haplotypes if it can be obtained as a combination of the two. This problem is NP-complete in the general case, but polynomially solvable for (k,l)-bounded instances for certain k and l. Here, k denotes the maximum number of ambiguous sites in any genotype, and l is the maximum number of genotypes that are ambiguous at the same site. Only the complexity of the (×, 2)-bounded problem is still unknown, where×denotes no restriction. It has been proved that (×,2)-bounded instances have compatibility graphs that can be constructed from cliques and circuits by pasting along an edge. In this paper, we give a constructive proof of the fact that (×,2)-bounded instances are polynomially solvable if the compatibility graph is constructed by pasting cliques, trees and circuits along a bounded number of edges. We obtain this proof by solving a slightly generalized problem on circuits, trees and cliques respectively, and arguing that all possible combinations of optimal solutions for these graphs that are pasted along a bounded number of edges can be enumerated efficiently.
| Original language | English |
|---|---|
| Article number | 7035191 |
| Pages (from-to) | 234-247 |
| Journal | IEEE/ACM Transactions on Computational Biology and Bioinformatics |
| Volume | 12 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2015 |
| Externally published | Yes |