Lecture 04-07-17

• Taken by rgli

How to deal with NP-completeness

• Approximation algorithms
• Algorithms that do not find the actual solution, but close to it
• In other fields, seen as an answer with a percent area of error
• Minimization algorithm
  • R_alg = max error over all inputs (solution found by algorithm / optimal solution)
• Bin packing
  • Next fit
    • 1 open bin, adds elements until overflow, shuts bin, opens new bin
  • R_NF < 2
    • Use even number of bins (1…2k)
    • Use odd number of bins (1…2k, 2k + 1)
    • Sum of a pair of bins > 1
    • If NF uses 2k bins then weight > K
    • Optimal = k + 1
    • 2k / (k + 1) < 2 and (2k + 1)/(k + 1) < 2
  • Variations
    • First fit: put new objects in 1st bin it fits in