Clustering a 2d Pareto Front: P-center Problems Are Solvable in Polynomial Time

Having many non dominated solutions in bi-objective optimization problems, this paper aims to cluster the Pareto front using Euclidean distances. The p-center problems, both in the discrete and continuous versions, become solvable with a dynamic programming algorithm. Having N points, the complexity of clustering is \(O(KN\log N)\) (resp. \(O(KN\log ^2 N)\)) time and O(N) memory space for the continuous (resp. discrete) K-center problem for \(K\geqslant 3\), and in \(O(N\log N)\) time for such 2-center problems. Furthermore, parallel implementations allow quasi-linear speed-up for the practical applications.

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