Programs for Estimating Lower Bounds on Reticulation Numbers of Networks for Multiple Phylogenetic Trees
  After downloading a program, you can run it as follows:
         program_name   TreeFile   [Time_Bound_in_Seconds]
where TreeFile contains two or more phylogenetic trees in Newick format, while Time_Bound_in_Seconds is an upper bound on the time that can be used to test if the RH bound (due to Y. Wu ) for the trees in TreeFile is at least as large as a given number.

   Time_Bound_in_Seconds may be omitted. In that case, there is no time bound on the testing and hence there is no time bound on the computation of the RH bound. We remark that computing the RH bound can take very long time (say, 1 day). This is why Time_Bound_in_Seconds can be helpful. No matter whether Time_Bound_in_Seconds is omitted or not, the programs always output the rMAAF bound for the trees in TreeFile. If Time_Bound_in_Seconds is 0, then the programs will stop immediately after computing the rMAAF bound. Otherwise, they will proceed to test if the RH bound is larger than i for i = L, L+1, ... (in this order), where L is the rMAAF bound.