We consider the model introduced by Bilu and Linial (2010)[13], who study problems for
which the optimal clustering does not change when distances are perturbed. They show that
even when a problem is NP-hard, it is sometimes possible to obtain efficient algorithms for
instances resilient to certain multiplicative perturbations, eg on the order of O (n) for max-cut
clustering. Awasthi et al.(2012)[6] consider center-based objectives, and Balcan and Liang
(2012)[9] analyze the k-median and min-sum objectives, giving efficient algorithms for …

We consider the model introduced by Bilu and Linial [12],, who study problems for which the
optimal clustering does not change when distances are perturbed. They show that even
when a problem is NP-hard, it is sometimes possible to obtain efficient algorithms for
instances resilient to certain multiplicative perturbations, eg on the order of for max-cut
clustering. Awasthi et al.[6], consider center-based objectives, and Balcan and Liang [9],
analyze the k-median and min-sum objectives, giving efficient algorithms for instances …