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Approximation Algorithms for Norm Multiway Cut
Charlie Carlson, Jafar Jafarov, Konstantin Makarychev +2
We consider variants of the classic Multiway Cut problem. Multiway Cut asks to partition a graph into parts so as to separate given terminals. Recently, Chandrasekaran…
Approximately counting independent sets in dense bipartite graphs via subspace enumeration
Charlie Carlson, Ewan Davies, Alexandra Kolla +1
We give a randomized algorithm that approximates the number of independent sets in a dense, regular bipartite graph -- in the language of approximate counting, we give an FPRAS for…
Computational thresholds for the fixed-magnetization Ising model
Charlie Carlson, Ewan Davies, Alexandra Kolla +1
The ferromagnetic Ising model is a model of a magnetic material and a central topic in statistical physics. It also plays a starring role in the algorithmic study of approximate co…
Lower bounds for Max-Cut in -free graphs via semidefinite programming
Charles Carlson, Alexandra Kolla, Ray Li +3
For a graph , let denote the size of the maximum cut in . The problem of estimating as a function of the number of vertices and edges of has a long history…
Improving the smoothed complexity of FLIP for max cut problems
Ali Bibak, Charles Carlson, Karthekeyan Chandrasekaran
Finding locally optimal solutions for max-cut and max--cut are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP m…
Optimal Lower Bounds for Sketching Graph Cuts
Charles Carlson, Alexandra Kolla, Nikhil Srivastava +1
We study the space complexity of sketching cuts and Laplacian quadratic forms of graphs. We show that any data structure which approximately stores the sizes of all cuts in an undi…