K-medoids clustering is solvable by dynamic programming in O(N 3) time for a 2D Pareto Front (PF). A key element is a interval clustering optimality. This paper proves this property holds also for local minima for k-medoids. It allows to enumerate the local minima of k-medoids with the same complexity than the computation of global optima for k=2 ou k=3. A pseudo-polynomial enumeration scheme is designed, for small values of k. This allows to understand results obtained by local search approaches in a 2D PF.