Syllabus (Tentative)

• General introduction. Matchings. Flows. LPs. Duality. Polyhedral characterizations of matchings. Basic graph theory around matching.
• Unweighted bipartite matching. Hofcroft-Karp.
• Hungarian algorithm for assignment problem.
• Scaling for faster assignment problem. Gabow-Tarjan
• Auction algorithm for matching.
• Parallel matching
  • Karp Upfal Wigderson ,
  • Mulmuley, Vazirani and Vazirani
  • Sublinear time algorithms for parallel matching. Goldberg Plotkin Vaidya.
  • Interior point algorithms -- Goldberg, Plotkin, Shmoys, Tardos
  • Maximal matchings using map-reduce
• Non-bipartite matching. Micali-Vazirani, Vazirani.
• Matchings and game theory.
• Stable Marriages.
• Average-case algorithms for matching. Motwani
• Clique partitions and accelerating matching. Motwani Feder
• Online b-matching . Kanasundaram Pruhs
• 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. Miirokni et. al.
• Learning in matching. Henzinger et. al.
• Online stochastic matching
• Other recent online matching results.
• Stable marriages.
• Applications of matchings
• Other topics.