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This paper examines a common extension of k-medoids and k-median clusteringin the case of a two-dimensional Pareto front, as generated by bi-objectiveoptimization approaches. A characterization of optimal clusters is provided,which allows to solve the optimization problems to optimality in polynomialtime using a common dynamic programming algorithm. More precisely, having $N$points to cluster in $K$ subsets, the complexity of the algorithm is proven in$O(N^3)$ time and $O(K.N)$ memory space when $K\geqslant 3$, cases $K=2$ havinga time complexity in $O(N^2)$. Furthermore, speeding-up the dynamic programmingalgorithm is possible avoiding useless computations, for a practical speed-upwithout improving the complexity. Parallelization issues are also discussed, tospeed-up the algorithm in practice.

k-medoids and p-median clustering are solvable in polynomial time for a 2d Pareto front