Cs 395t: Algorithms for Computational Biology 12.2 Applications of Dynamic Programming (hw) 12.2.1 Computing the Topological Diameter of a Tree

Each student should select a paper to present to the class and notify Professor Warnow of this selection by e-mail prior to next Tuesday's lecture. Scribe Notes. Beginning with today's lecture, a designated scribe will be responsible for taking notes on each lecture, typesetting a polished and thorough version of the notes in L A T E X, e-mailing the notes in both .tex and .pdf formats to Professor Warnow, and revising the notes to incorporate the profes-sor's feedback. Both problems on Homework #2 were concerned with applications of dynamic programming to bioinformatics tasks. This section briefly outlines solutions to these problems: Problem 1. Give a dynamic programming algorithm for computing the longest leaf-to-leaf path in a tree. (Here we define the length of a path to be the number of edges in the path.) This is also called the " topological diameter " of the tree. Analyze the running time. Problem 2. Give a dynamic programming algorithm for the longest common subsequence between two strings. This is the same problem as finding the minimum number of deletions from the two strings so that the result is two identical strings. Thus, the longest common subsequence of AAAAAAAAAA and CATTAGAA is AAAA. Analyze the running time. To find the topological diameter of a tree, we first define H(n), the height of a node n ∈ N to represent the maximum number of edges from a leaf node it is: 12-1