On the practically interesting instances of MAXCUT
Yonatan Bilu, Amit Daniely, Nati Linial, Michael Saks · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2013
For many optimization problems, the instances of practical interest often occupy just a tiny part of the algorithm's space of instances. Following (Y. Bilu and N. Linial, 2010), we apply this perspective to MAXCUT, viewed as a clustering problem. Using a variety of techniques, we investigate practically interesting instances of this problem. Specifically, we show how to solve in polynomial time distinguished, metric, expanding and dense instances of MAXCUT under mild stability assumptions. In particular, (1 + epsilon)-stability (which is optimal) suffices for metric and dense MAXCUT. We also show how to solve in polynomial time Omega(sqrt(n))-stable instances of MAXCUT, substantially improving the best previously known result.