Randomness and Relaxation

• Reduce problem to integer programming or integer semi-definite programming. (Goemans and Williamson, 1994)

  • Relax to linear programming or semi-definite programming yielding a non-integer solution. There are polynomial time algorithm for LP and SDP.
  • Randomized rounding to achieve a good integer solution.
  • Provable bounds on approximation.

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