(the topic sounds interesting, I don't know anything about the
speaker, sorry)
-------- Forwarded Message --------
Dear Colleagues,
Prof. Kavitha Telikepalli (TIFR, India) will be giving a
mini-course on popular matchings at USPN.
You are invited to attend, it will be broadcast at this link:
Please find below an abstract of the mini-course.
Best wishes,
Nabil
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Lecture 1, Tuesday 07/05 at 16h : Introduction to popular
matchings.
The problem of computing a stable matching in a bipartite
graph is an old and well-studied problem. Gale and Shapley
showed in 1962 that such a matching always exists and can be
efficiently computed. This is a classical result in algorithms
with many applications in economics and computer science.
Stability is a strong and rather restrictive notion. This series
of talks will be on a relaxation of stability called
"popularity". In the first talk we will see simple and efficient
algorithms for some popular matching problems. No background in
algorithms or matching theory will be assumed.
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Lecture 2, Tuesday 14/05 at 14h: Popular matchings and
optimality.
In this talk we will consider algorithms for finding optimal
popular matchings. While it is easy to find max-size popular
matchings, it is NP-hard to find a min-cost popular matching.
This motivates us to relax popularity to a weaker notion called
"quasi-popularity". Describing the popular and quasi-popular
matching polytopes is hard, but there is an easy-to-describe
integral polytope sandwiched between these two hard ones. So we
can efficiently find a quasi-popular matching of cost at most
that of a min-cost popular matching.
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Lecture 3, Tuesday 21/05 at 14h: Popular assignments and
extensions.
This talk will be on popular matchings in the one-sided
preferences model. Popular matchings need not always exist in
this model and there is a simple combinatorial algorithm to
decide if one exists. We will see an LP-duality inspired
algorithm for the more general problem of deciding if a popular
assignment (i.e., a popular maximum-matching) exists or not.
This algorithm can be generalized to solve the popular common
base problem in the intersection of two matroids where one
matroid is the partition matroid, this implies the popular
arborescence problem (relevant in liquid democracy) can be
solved efficiently.