Re: [theory students] Theory lunch and TCS+ in TEN MINUTES in 2310 (Nima Anari)

[Benjamin Miller <bmiller@xxxxxxxxxxx>]

Hi all,

Just a reminder that this is happening in 10 minutes!

Benjamin

On Wed, Mar 14, 2018 at 12:02 AM, Benjamin Miller <bmiller@xxxxxxxxxxx> wrote:

Hi all,

Sorry for the late notice. We'll have theory lunch at noon today in CS 2310. Nima Anari of Stanford will be giving a TCS+ talk onÂ"Planar Graph Perfect Matching is in NC" (abstract below). See you there!

Benjamin

Planar Graph Perfect Matching is in NC

Abstract: Is matching in NC? In other words, is there a deterministic fast parallel algorithm for it? This has been an open question for over three decades, ever since the discovery of Random NC matching algorithms. Within this question, the case of planar graphs had remained an enigma: On one hand, counting the number of perfect matchings is generally believed to be 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, 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. Paper available at: https://arxiv.org/pdf/1709.07822.pdf

Joint work with Vijay Vazirani.

Joint work with Vijay Vazirani.