{"paper":{"title":"Self-improving Algorithms for Coordinate-wise Maxima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"C. Seshadhri, Kenneth L. Clarkson, Wolfgang Mulzer","submitted_at":"2012-04-03T22:42:57Z","abstract_excerpt":"Computing the coordinate-wise maxima of a planar point set is a classic and well-studied problem in computational geometry. We give an algorithm for this problem in the \\emph{self-improving setting}. We have $n$ (unknown) independent distributions $\\cD_1, \\cD_2, ..., \\cD_n$ of planar points. An input pointset $(p_1, p_2, ..., p_n)$ is generated by taking an independent sample $p_i$ from each $\\cD_i$, so the input distribution $\\cD$ is the product $\\prod_i \\cD_i$. A self-improving algorithm repeatedly gets input sets from the distribution $\\cD$ (which is \\emph{a priori} unknown) and tries to op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0824","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":""},"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"}