Assigned:
Thursday, April 28, 2016
Due:
Do not hand in
General Instructions
- Please review the
course information.
- You must write down with whom you worked on the assignment. If this
changes from problem to problem, then you should write down this
information separately with each problem.
- Numbered problems are all from the textbook Network Flows .
Problems
- Show that a greedy algorithm for vertex cover (repeatedly take
the vertex of maximum degree) can give a solution that is more than twice optimal.
- The closest point heuristic for the travelling salesman problem
works as follows. You start with a 1 node "tour" T. At each step,
you pick the node closest to the current tour T (that is the one with
minimum distance to a vertex v on the tour) and add it to the tour as
a neighbor of v. You stop when all vertices are on the tour. Show
that this algorithm is a 2-approximation for travelling salesman with
triangle inequality.
- Give a O(ln n) approximation algorithm for the weighted set cover problem and analyze the algorithm. In this problem, each set S has a weight w(S) and you want to choose the set of minimum total weight that is a cover.
- Give a polynomial time algorithm for vertex cover in a bipartite graph. (Hint: use ideas from flow and matching).
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