*********************************
There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
*********************************
Algorithms & Randomness Center (ARC)
Anupam Gupta (CMU)
Monday, October 18, 2021
Klaus 1116 East - 11:00 am
Title: Finding and Counting k-cuts in Graphs
Abstract: For an undirected graph with edge weights, a k-cut is a set of edges whose deletion breaks the graph into at least k connected components. How fast can we find a minimum-weight k-cut? And how many minimum k-cuts can a graph have? The two problems are closely linked. In 1996 Karger and Stein showed how to find a minimum k-cut in approximately n^{2k-2} time; their proof also bounded the number of minimum k-cuts by n^{2k-2}, using the probabilistic method. Prior to our work, these were the best results known. Moreover, both these results were not known to be tight, except for the case of k=2 (which is the classical problem of finding graph min-cuts).
In this talk, we show how both these results can be improved to approximately n^k. We discuss how extremal bounds for set systems, plus a refined analysis of the Karger's contraction algorithm, can give near-optimal bounds.
This is joint work with Euiwoong Lee (U.Michigan), Jason Li (CMU), and David Harris (Maryland).
----------------------------------
Videos of recent talks are available at: https://smartech.gatech.edu/handle/1853/46836
Click here to subscribe to the seminar email list: arc-colloq@Klauscc.gatech.edu
