Phylogenetic network is a way to describe evolutionary histories that have undergone evolutionary events such as recombination, hybridization, or horizontal gene transfer. The level, k, of a network determines how non-treelike the evolution can be, with level-0 networks being trees. A number of methods for constructing rooted phylogenetic network from triplets have been proposed in the past.1,2 In this issue, Gambette et al.3 discuss how to generalize these methods to construct unrooted phylogenetic network from quartets. The paper has three main contributions: (1) it gives an Oðn 5 ð1 þ ðn; nÞÞÞ time algorithm to compute the set of quartets of a network; (2) it shows that level-1 quartet consistency is NP-hard; and (3) given a set Q of quartets, it shows that Oðn 4 Þ time is su±cient to compute the unrooted level-1 network N such that Q ¼ QðNÞ, if it exists.Modern DNA sequencers produce an explosive amount of sequence data of relatively short read lengths. A number of fast genome mapping tools, which use the BurrowsÀWheeler transforms 4 for seed search and dynamic programming for ex-