Home Work 5
This Home work is on Shortest path Algorithms a(Chapter 4 of Das Gupta) and
Greedy Algorithms (Chapter 5 of Das Gupta) and Chapter 6(Dynamic Programming) Optional problems are not to
be submitted Do any 6 problems and choose at least one problem from each topic
(shortest path algorithm, greedy algorithm, dynamic programming) Due on 4/16/2015.
- Do Problem 4.13 a (DG)
- Do Problem 4.19 (DG)
- Do Problem 4.21 a (DG)
- Problem 24.3.6 (CLRS Edition 3 Page 603 - the problem is given below)
We are given a directed graph G =(V,E) on which each edge (u,v) in E has an
associated value r(u,v), which is a real number in the range 0 ≤ r(u,v) ≤ 1
that represents the reliability of a communication channel from vertex
u to vertex v. We interpet r(u,v) as the probability that the channel from u
to v will not fail and we assume that these probabilities are
independent. Give an efficient algorithm to find the most reliable path
between two given vertices.
- Problem 5.5 (DG)
- Problem 5.7 (DG)
- Problem 5.8 (DG)
- Prolem 5.14 (DG)
- Do Problem 5.20 (DG) - find a perfect matching in a tree
- Do Problem 5.21 (DG) - find a minimum feedback edgeset in a weighted undirected graph (This problem is at the end of 5.20(DG) in the pDF version - Two problems are given as one problem in the PDF version - that is a typo)
- Problem 5.32 (DG) (This is problem 5.31 in the PDF version - the problem numbers are mixed up because of the earlier typo - I think)
- Do Problem 6,3 (DG)
- Do Problem 6.5 (DG)
- Do Problem 6.17 (DG)
- Optional Do not submit Do Problem 4.2 (DG)
- Optional Problem 5.1 (DG)
- Optional Problem 5.2 (DG)