Syllabus (Tentative)

• General introduction. Matchings. Flows. LPs. Duality.
• Unweighted bipartite matching. Hofcroft-Karp.
• Hungarian algorithm for assignment problem.
• Scaling for faster assignment problem. Gabow-Tarjan
• Polyhedral characterizations of matchings. Basic graph theory around matching.
• Non-bipartite matching.
  • Michel Goeman's notes on non-bipartite matching
  • Efficient implementation of non-bipartite matching
  • reductions and approximate matching
• Faster matching via electrical flows
  • Madry matching paper
  • Madry flow paper
• Parallel/distributed/streaming matching
  • Mulmuley, Vazirani and Vazirani
  • Maximal matchings using map-reduce
  • Using coresets
  • Approximate Maximum Matching using mapreduce (1)
  • Approximate Maximum Matching using mapreduce (2)
  • McGregor
  • Matchings in a semi-streaming model
  • Streaming, LP, Mulitplicative Weights and Matching
  • 2-approximation in streaming
• Matchings with recourse
  • Bouding the Number of flips
  • Bounding Flips in Near Matchings
  • Load Balancing in p-norm
• Dynamic Matchings.
  • Sublinear Time
  • Fast Update Time
  • Primal Dual
  • Log Update Time
  • bipartite, sub 2-approx
• Stable Marriages.
  • Popular Matchings
  • Popularity vs. Fairness
  • Fair Matchings
• Kidney Exchanges and related applications.
  • Tim Roughgarden's notes paper by Alvin Roth
• Random Matchings
  • Average-case algorithms for matching.
  • Karp Sipers random graph matching
• Adwords
  • Online b-matching .
  • Adwords problem. Metha et. al.
  • Online primal-dual for adwords. Buchbinder Jain.
  • Stochastic adwords problem. Feldman et. al.
  • Getting both a stochastic and a determistic guarantee. Mirokni et. al.
• Learning in matching. Henzinger et. al.
• Applications of matchings
• Other topics.