Matchings
Overview
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:
- Classic results on matching problems.
- scaling algorithms
- massively parallel algorithms
- distributed algorithms
- average case analysis
- fast approximations
- online algorithms
- dynamic algorithms
- stochastic algorithms
- algorithms using learning
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.
Information
Homework
Lecture Schedule
- 9/17 - Introduction. Matching algorithms. Duality.
- 9/24 - Effiicent matching algorithms.
- 9/28 - Finish Hungarian algorithm. Gabow Tarjan.
- 10/8 - finish gabow-tarjan, non-bipartite matchings
- 10/15 - parallel matchings, introduction to map reduce model, EDCS and parallel model
- 10/22 - Streaming
- Xingyu Zhang.
Graph problems in a semi streaming model.
- Austin Palmer.
Matchings in a semi-streaming model
- 10/29 - Dynamic Matchings
- Oussama Hanguir. Primal Dual
- Philippe Mizrahi. Log Update Time
- 11/12 Adwords (1)
- Jingtong Zhao. Adwords problem. Metha et. al.
- Omar El Housni. Online primal-dual for adwords. Buchbinder Jain.
- 11/19 Adwords (2)
- Michael Hamilton. Stochastic adwords problem. Feldman et. al.
- Sai Mali. Getting both a stochastic and a determistic guarantee. Mirokni et. al.
- 11/26 Stable/Popular/Fair Matchings (1)
- Lingyi Zhang. Popularity vs. Fairness
- Jia Wan.
A Fixed Point Approach to Stable Matchings and Some Applications
- 12/3 Stable/Popular/Fair Matchings (2)
- Xujia Lui . Popular Matchings
- Xuan Zhang. Fair Matchings
- 12/10. (Plus some other data TBA)
- Victor Lacomte. Madry flow paper
- Xiao Lei. paper by Alvin Roth
- Yeqing Zhou. Bouding the Number of flips
Course Announcements
- No lecture on September 10. First lecture on September 17.