Answer the following questions. Refer to the textbook and lecture notes (ppt presentations).

1. If D is an additive distance matrix, then for any i, j, k, D_i,j + D_j,k ≥ D_{i, k}. Please explain why this is true.

2. Show how algorithm AdditivePhylogeny works by showing the steps that produce the phylogeny in (b) given the matrix D in (a) in the following figure.

   

3. Demonstrate an example (different from those given in the text and ppt presentations) to show how Sankoff Algorithm constructs a character-based phylogenetic tree of depth at least 2 (with non-unit distance matrix).

4. Show that Sankoff Algorithm and Fitch Algorithm yield the same result for your example for the previous question, assuming the unit distance matrix is used.

5. Use an example to show differences between Lloyd's algorithm and the ProgressiveGreedy algorithm for K-Mean.

This homework is due on Thursday April 7, 2016.