Given two binary trees on N labeled leaves, the quartet distance between the trees is the number of disagreeing quartets. By permuting the leaves at random, the expected quartets distance between the two trees is 2 3 N 4 . However, no strongly explicit construction reaching this bound asymptotically was known.We consider complete, balanced binary trees on N = 2 n leaves, labeled by n long bit sequences. Ordering the leaves in one tree by the prefix order, and in the other tree by the suffix order, we show that the resulting quartet distance is 2 3 + o(1) N 4 , and it always exceeds the 2 3 N 4 bound.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.