Perfect Phylogeny Haplotyping is Complete for Logspace

Haplotyping is the bioinformatics problem of predicting likely haplotypes based on given genotypes. It can be approached using Gusfield’s perfect phylogeny haplotyping (PPH) method for which polynomial and linear time algorithms exist. These algorithm use sophisticated data structures or do a stepwise transformation of the genotype data into haplotype data and, therefore, need a linear amount of space. We are interested in the exact computational complexity of PPH and show that it can be solved space-efficiently by an algorithm that needs only a logarithmic amount of space. Together with the recently proved L-hardness of PPH, we establish L-completeness. Our algorithm relies on a new characterization for PPH in terms of bipartite graphs, which can be used both to decide and construct perfect phylogenies for genotypes efficiently.