{"paper":{"title":"Exact Algorithms for Minimum Steiner Point Trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Donghoon Shin, Eungyu Woo","submitted_at":"2026-08-01T17:51:30Z","abstract_excerpt":"Given distinct terminals $P\\subset R^2$ and $R>0$, the Steiner tree problem with minimum number of Steiner points and bounded edge length asks for a straight line tree spanning $P$, with every edge of length at most $R$, that minimizes the number of Steiner points. Length is measured in a fixed $L_p$ metric with $p\\in Q_{\\ge 1}\\cup\\{\\infty\\}$. The optimum $k$ is not bounded by $n$, even in two-terminal case.\n  We give a deterministic exact algorithm that computes an optimal implicit representation in $n^{O(n)}$ time, independent of $k$, in the computation model of Section~\\ref{subseccomputatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00795","kind":"arxiv","version":1},"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/2608.00795/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"}