Consensus Tree under the Ancestor-Descendant Distance is NP-hard

Abstract

Due to uncertainty in tumor phylogeny inference from sequencing data, many methods infer multiple, equally-plausible phylogenies for the same cancer. To summarize the solution space 𝒯 of tumor phylogenies, consensus tree methods seek a single best representative tree S under a specified pairwise tree distance function. One such distance function is the ancestor-descendant (AD) distance d (T, T′), which equals the symmetric difference of the transitive closures of the edge sets E (T) and E (T′). Here, we show that finding a consensus tree S for tumor phylogenies 𝒯 that minimizes the total AD distance ∑_{T ∈𝒯} d (S, T) is NP-hard.