Abstract
Parsimony haplotyping is the problem of finding a smallest size set of haplotypes that can explain a given set of genotypes. The problem is NP-hard, and many heuristic and approximation algorithms as well as polynomial-time solvable special cases have been discovered. We propose improved fixed-parameter tractability results with respect to the parameter “size of the target haplotype set” k by presenting an O *(k 4k)-time algorithm. This also applies to the practically important constrained case, where we can only use haplotypes from a given set. Furthermore, we show that the problem becomes polynomial-time solvable if the given set of genotypes is complete, i.e., contains all possible genotypes that can be explained by the set of haplotypes.
Supported by the DFG, research projects PABI, NI 369/7, and DARE, GU 1023/1, NI 369/11, NSF China (No. 60973026), Shanghai Leading Academic Discipline Project (project number B114), Shanghai Committee of Science and Technology of China (nos. 08DZ2271800 and 09DZ2272800), the Excellence Cluster on Multimodal Computing and Interaction (MMCI), and Robert Bosch Foundation (Science Bridge China 32.5.8003.0040.0).
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Fleischer, R. et al. (2010). Extended Islands of Tractability for Parsimony Haplotyping. In: Amir, A., Parida, L. (eds) Combinatorial Pattern Matching. CPM 2010. Lecture Notes in Computer Science, vol 6129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13509-5_20
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DOI: https://doi.org/10.1007/978-3-642-13509-5_20
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