Planar p-center problems are solvable in polynomial time when clustering a Pareto Front

08/19/2019

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by   Nicolas Dupin, et al.

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This paper is motivated by real-life applications of bi-objective optimization. Having many non dominated solutions, one wishes to cluster the Pareto front using Euclidian distances. The p-center problems, both in the discrete and continuous versions, are proven solvable in polynomial time with a common dynamic programming algorithm. Having N points to partition in K≥ 3 clusters, the complexity is proven in O(KNlog N) (resp O(KNlog^2 N)) time and O(KN) memory space for the continuous (resp discrete) K-center problem. 2-center problems have complexities in O(Nlog N). To speed-up the algorithm, parallelization issues are discussed. A posteriori, these results allow an application inside multi-objective heuristics to archive partial Pareto Fronts.