[Facets-of-complexity] Invitation Special Talk Friday - changed Abstract

[Ita Brunke <i.brunke@inf.fu-berlin.de>]

You are cordially invited to our special talk on Friday 12th of July at TU Berlin.

Special Lecture on Friday, 12th of July, at TU Berlin:

Location:

Room MA 041 - Ground Floor
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin

Time: Friday, July 12th - 10:15 h

Lecture: Vijay Vazirani (University of California)

Title: Matching is as Easy as the Decision Problem, in the NC Model

Abstract:

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. Over the last five years, the TCS community has launched a relentless attack on this question, leading to the discovery of numerous powerful ideas. We give what appears to be the culmination of this line of work: An NC algorithm for finding a minimum weight perfect matching in a general graph with polynomially bounded edge weights, provided it is given an oracle for the decision problem. Consequently, for settling the main open problem, it suffices to obtain an NC algorithm for the decision problem. We believe this new fact has qualitatively changed the nature of this open problem.

All known efficient matching algorithms for general graphs follow one of two approaches: those initiated by Edmonds (1965) or Lovasz (1979). Our algorithm is based on a new approach which was inspired by the multitude of ideas discovered in the last five years.

The difficulty of obtaining an NC perfect matching algorithm led researchers to study matching vis-a-vis clever relaxations of the class NC. In this vein, Goldwasser and Grossman (2015) gave a pseudo-deterministic RNC algorithm for finding a perfect matching in a bipartite graph, i.e., an RNC algorithm with the additional requirement that on the same graph, it should return the same (i.e., unique) perfect matching for almost all choices of random bits. A corollary of our reduction is an analogous algorithm for general graphs.
This talk is fully self-contained. Based on the following joint paper with Nima Anari: https://arxiv.org/pdf/1901.10387.pdf