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 low dimensions. Another contribution is a simple and efficient algorithm for building explainable clusterings for the k-means problem. We provide empirical evidence that its performance is better than the current state of the art for decision-tree based explainable clustering .