Before revision:   We provide upper and lower bounds on this price as well as efficient algorithms to build explainable clustering for the k-means, k-medians, k-center and the maximum-spacing problems in a natural model in which explainability is achieved via decision trees  ]  .
After revision:  We provide upper and lower bounds on this price as well as efficient algorithms to build explainable clustering for the k-means, k-medians, k-center and the maximum-spacing problems in a natural model in which explainability is achieved via decision trees . For the k-means and k-medians problems our upper bounds improve those obtained by ] .