{"paper":{"title":"Polynomial-Time Riesz-Energy Subset Selection for Ordered Point Sets on Lines and $\\ell_1$-Staircases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Michael T.M. 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. When feasible subsets are encoded as increasing index vectors, this property implies submodul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.16946","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.16946/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}