More Like this

1. Multicriteria cuts and size-constrained k-cuts in hypergraphs

   https://doi.org/10.1007/s10107-021-01732-0  

   Beideman, Calvin; Chandrasekaran, Karthekeyan; Xu, Chao (November 2021, Mathematical Programming)
2. Approximating Small Sparse Cuts

   https://doi.org/10.1145/3618260.3649747  

   Anand, Aditya; Lee, Euiwoong; Li, Jason; Saranurak, Thatchaphol (June 2024, Proceedings of the annual ACM Symposium on Theory of Computing)
3. From Graph Cuts to Isoperimetric Inequalities: Convergence Rates of Cheeger Cuts on Data Clouds

   https://doi.org/10.1007/s00205-022-01770-8  

   García Trillos, Nicolás; Murray, Ryan; Thorpe, Matthew (April 2022, Archive for Rational Mechanics and Analysis)

   Abstract In this work we study statistical properties of graph-based clustering algorithms that rely on the optimization of balanced graph cuts, the main example being the optimization of Cheeger cuts. We consider proximity graphs built from data sampled from an underlying distribution supported on a generic smooth compact manifold$${\mathcal {M}}$$ $M$. In this setting, we obtain high probability convergence rates for both the Cheeger constant and the associated Cheeger cuts towards their continuum counterparts. The key technical tools are careful estimates of interpolation operators which lift empirical Cheeger cuts to the continuum, as well as continuum stability estimates for isoperimetric problems. To the best of our knowledge the quantitative estimates obtained here are the first of their kind. 

   more » « less
4. Split Cuts in the Plane

   https://doi.org/10.1137/20M1324521  

   Basu, Amitabh; Conforti, Michele; Di Summa, Marco; Jiang, Hongyi (January 2021, SIAM Journal on Optimization)

   null (Ed.)
5. Hypergraph cuts above the average

   https://doi.org/10.1007/s11856-019-1897-z  

   Conlon, David; Fox, Jacob; Kwan, Matthew; Sudakov, Benny (August 2019, Israel Journal of Mathematics)