IEOR 8100 Matchings
Fall 2012


Professor Cliff Stein


Matchings play a central role in algorithms, optimization and combinatorics. There are many variants of matching problems and they arise in a large number of applications. We will study a series of algorithms for matching and its extensions. Because of the central role that matching problem have played, there are a wide range of algorithms and by studying matchings, we will learn many interesting techniques that are widely applicable to other graph and combinatorial problems. Specific topics studied will include: We will also study several applications. The most prevalent will be matching problems that arise in internet advertising, as these applications have inspired some of the most interest algorithmic work on matching in the last several years.



Lecture Notes

  1. 9/4. Introduction.
  2. 9/6. Fractional Perfect Matchings.
  3. 9/11. Perfect Matching Polytope.
  4. 9/13. Matchings on Bipartite Graphs
  5. 9/20. Hopkroft Karp
  6. 9/25. Hungarian Algorithm.
  7. 9/27. Gabow Tarjan scaling algorithm.
  8. 10/2. Gabow Tarjan scaling algorithm (2).
  9. 10/4. Auction Algorithm.
  10. 10/11. Auction Algorithms. Parallel algorithms.
  11. 10/16. Parallel algorithms for Matching.
  12. 10/18. Parallel algorithms for Matching.
  13. 10/23. MapReduce algorithms for Matching
  14. 10/25. MapReduce algorithms for Matching.
  15. 11/1. Matching in a random graph.

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