Seminars and Colloquia by Series

Thursday, November 16, 2017 - 13:30 , Location: Skiles 005 , Vijay Vazirani , UC Irvine , Organizer: Robin Thomas

Is matching in NC, i.e., is there a deterministic fast parallel
algorithm for it? This has been an outstanding open question in TCS for
over three decades, ever since the discovery of Random NC matching
algorithms. Within this question, the case of planar graphs has remained
an enigma: On the one hand, counting the number of perfect matchings is
far harder than finding one (the former is #P-complete and the latter
is in P), and on the other, for planar graphs, counting has long been
known to be in NC whereas finding one has resisted a solution!The
case of bipartite planar graphs was solved by Miller and Naor in 1989
via a flow-based algorithm. In 2000, Mahajan and Varadarajan gave an
elegant way of using counting matchings to finding one, hence giving a
different NC algorithm.However, non-bipartite
planar graphs still didn't yield: the stumbling block being odd tight
cuts. Interestingly enough, these are also a key to the solution: a
balanced odd tight cut leads to a straight-forward divide and conquer NC
algorithm. The remaining task is to find such a cut in NC. This
requires several algorithmic ideas, such as finding a point in the
interior of the minimum weight face of the perfect matching polytope and
uncrossing odd tight cuts.Joint work with Nima Anari.

Tuesday, January 19, 2016 - 13:05 , Location: Skiles 006 , Shuji Kijima , Kyushu University , Organizer: Prasad Tetali
The rotor-router model, also known as the Propp machine,

is a deterministic process analogous to a simple random walk on a graph.

In this talk, we are concerned with a generalized model, functional-router

model, which imitates a Markov chain possibly containing irrational transition

probabilities. We investigate the discrepancy of the number of tokens

between the functional-router model and its corresponding Markov chain,

and give some upper bounds in terms of the mixing time of the Markov chain.