Lecture 2-1-17

Describe a problem (has a famous name)

• Form of connecting networks
• Everything came through the telephone
• Connect everyone so that there is a path between all pairs
• Goal:
  • minimize cost
  • develop a “good” algorithm for deciding how to connect people

Ideas

• Has to do with spanning tree (only factor is cost, length doesn’t matter)
  1. Order edges by cost and check if path exists, if not add.
  2. Start from a random vertex and add vertices based on minimum cost to adjacent neighbors
  3. Horrible:
  • Powerset of all edges and keep track of minimum of the ones that are connected
    1. Little less horrible:

Other Ideas

• Find cycles

Considerations

• Correctness
  • least possible cost (not just connected)
• Fastest

Greedy Algorithms

• Characteristics
  • Natural & easy to understand
  • Fast
  • Often times incorrect
• How to prove (always have to)
• Definition
  • Once it adds to solution, it never goes back
• Side notes
  • Greedy removal: once it throws it away, never gives back
  • Local improvement: start with a solution (which might be bad) and look to improve