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Table 1 Complexities of \({\mathbf{pf}}\) operators

From: Pareto optimization in algebraic dynamic programming

Operator Worst case Expected case
\({\mathbf{pf}}_\text {sort}\) \(O(N \log N)\) \(O(N \log N)\)
\({\mathbf{pf}}_\text {isort}\) \(O(N^2)\) \(O(N \log N)\)
\({\mathbf{pf}}_\text {lex}\) O(N) O(N)
\({\mathbf{pf}}_\text {smooth}\) \(O(N^2)\) \(O(N \log N)\)
\({\mathbf {pf}}_\text {nosort}\) \(O(N^2)\) \(O(N \log N)\)