Fig. 2.

Cutting plane and column generation enables SPhyR to efficiently solve practical k-DP instances. We show results for m × n binary matrices $B=[b_{p,c}]$ where m = n. (a) The number of solved instances for varying dimensions and maximum number k of character losses. For each k and m × n, there are 60 simulated instances. SPhyR solved all k = 1 instances (blue) to optimality, but exceeded the run time limit for k = 3 instances (red) with dimensions 100 × 100. (b) The run time in seconds (logarithmic scale) increased with increasing k and m × n. (c) The fraction of entries $b_{p,c}=0$. (d) The percentage of model variables $a_{p,c,i}$ instantiated during column generation. (e) The percentage of model constraints (logarithmic scale) added during separation. (f) The number of column generation iterations. Only a single iteration is required if B is a perfect phylogeny matrix