...led X in T . Output the resulting network. Notice that Steps 1, 3 and 4 are similar to the corresponding steps in algorithms for constructing galled trees (i.e. level-1 networks) and galled networks (=-=Huson and Klöpper, 2007-=-; Huson et al., 2009; D.H.Huson et al., submitted for publication). The reason why we use the same set-up in our algorithm, is outlined by Theorem 1. It shows that, when constructing a level-k network...

...rk is bounded by a constant. We have implemented Cass and added it to our popular treedrawing program Dendroscope (Huson et al., 2007), where it can be used as an alternative for the cluster network (=-=Huson and Rupp, 2008-=-) and galled network (Huson et al., 2009) algorithms. Experiments show that, although Cass needs more time than these other algorithms, it constructs a simpler network representing the same set of clu...

...s. Thus, mathematically speaking, such a node has indegree 1 and outdegree at least 2. In recent years, a lot of work has been done on developing methods for computing (rooted) phylogenetic networks (=-=Gambette, 2009-=-; Gusfield et al., 2007b; D.H.Huson et al., submitted for publication; Nakleh, 2009; Semple, 2007), which form a generalization of phylogenetic trees. Next to nodes representing speciation, rooted phy...