Combinatorial Optimization

K. Subramani, LCSEE, West Virginia University March 13, 2013

1. Review of Max Flows.

2. The Minimum Spanning tree problem.

3. File storage problem. Cost of accessing k^{th} file is cost(k) = ∑_{i=1}^{k} l_{i}. Assuming all files are equally likely to be accessed, we define E[cost] = ∑_{k=1}^{n} \frac{cost[k]}{n} = ∑_{k=1}^{n} ∑_{i=1}^{k} \frac{l_{i}}{n}.

4. Scheduling tasks to minimize the number of machines. Start time, finish time, conflicting schedule.

5. Scheduling tasks to maximize the number of tasks, given a fixed set of machines.

6. The fractional knapsack problem.

7. The theory underlying greedy algorithms.

8. Independence axioms.