IEOR 6614, Spring 2016 : Homework 12

Assigned: Thursday, April 28, 2016
Due: Do not hand in

General Instructions

  1. Please review the course information.
  2. 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.
  3. Numbered problems are all from the textbook Network Flows .

Problems

  1. 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.
  2. 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.
  3. 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.
  4. Give a polynomial time algorithm for vertex cover in a bipartite graph. (Hint: use ideas from flow and matching).


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cliff@ieor.columbia.edu