Lecture 04-17-17

Test

• 3 questions on complexity classes:
  1. Reduction
  2. Understanding
     • What it means to be in NP/NP-complete
  3. Approximation/reduction
     • could be branch and bound
  4. DP
     • DP that was almost on the test
       • Optimal matrix chain / optimal binary search
       • Explain the difference that let one be solved in O(N^2) vs
       • Answer: could not move the root to the left
• Branch & bound: on it only in relation to approximation
• Two times optimal for TSP
  • Build MST and traverse in DFS
  • With a triangle inequality? Did not cover this semester

Local improvement

• Example: TSP
• Example: Greedy vertex cover
  • Improvements
    • Are all vertices needed?
    • Can I add 2 and get rid of 3?
      • Swapping algorithms

Max Flow

• What’s flowing?
• Digraph
• Can always create:
  • Just assign 0’s to everything
• Flow is measured
• Cut is a division of the vertices
• Can measure flow across any cut