Title:
Finding and Counting k-cuts in Graphs
Finding and Counting k-cuts in Graphs
Author(s)
Gupta, Anupam
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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).
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Date Issued
2021-10-18
Extent
58:52 minutes
Resource Type
Moving Image
Resource Subtype
Lecture