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Given $x_1<\\cdots<x_n$, an exponent $s>0$, and a cardinality $k$, the task is to choose $1\\leq i_1<\\cdots<i_k\\leq n$ minimizing $E_s(i_1,\\ldots,i_k)=\\sum_{1\\leq p<q\\leq k}(x_{i_q}-x_{i_p})^{-s}$. We prove that the one-dimensional Riesz interaction satisfies a Monge inequality. 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Emmerich","submitted_at":"2026-06-15T16:46:32Z","abstract_excerpt":"We study efficient algorithms for one-dimensional fixed-cardinality minimum Riesz $s$-energy subset selection on ordered real-line point sets and propose and test a polynomial-time exact s-t cut-based algorithm for this problem. Given $x_1<\\cdots<x_n$, an exponent $s>0$, and a cardinality $k$, the task is to choose $1\\leq i_1<\\cdots<i_k\\leq n$ minimizing $E_s(i_1,\\ldots,i_k)=\\sum_{1\\leq p<q\\leq k}(x_{i_q}-x_{i_p})^{-s}$. We prove that the one-dimensional Riesz interaction satisfies a Monge inequality. 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