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On June 15-16, 2017 Stephen Fenner (University of South Carolina) will give a mini-course "The matching problem: Approaches, applications, and algorithms".
Address: Faculty of computer science, Kochnovsky proezd, 3.
15.06.2017 18:10-19:30 (room 317)
16.06.2017 16:40-19:30 (room 317)
Participation is free, but the registration is needed.
If you have questions, please contact the manager of the laboratory Ekaterina Vavilova: email@example.com.
The matching problem in graphs is central to graph theory and combinatorics, with a host of related problems and connections. In this minicourse, we will discuss historical approaches to this problem, including Koenigs Minimax theorem (which ties together several results, including the Marriage theorem and Halls theorem), as well as the problems connection to matrix determinants, network flows and cuts, matroids (time permitting) and geometry (such as the matching polytope). We will review fast sequential algorithms for matching, including the reduction to max flow for bipartite graphs and Edmondss algorithm for matching in general graphs. Finally, we look at newer ways to parallelize matching algorithms, including the Isolation lemma and its use in finding fast, randomized parallel algorithms for matching, and new geometry-based ways to partially derandomize these algorithms.