Nearly tight bounds on the price of explainability for the k-center and the maximum-spacing clustering problems

The price of explainability for a clustering task can be defined as the unavoidable loss, in terms of the objective function, if we force the final partition to be explainable. Here, we study this price for the k-centers and maximum-spacing clustering problems. We provide nearly tight bounds for a natural model where explainability is achieved via decision trees.