{"paper":{"title":"Monotone Contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Eleni Batziou, John Fearnley, Rahul Savani, Ruta Mehta, Spencer Gordon","submitted_at":"2024-11-15T11:07:05Z","abstract_excerpt":"We study functions $f : [0, 1]^d \\rightarrow [0, 1]^d$ that are both monotone and contracting, and we consider the problem of finding an $\\varepsilon$-approximate fixed point of $f$. We show that the problem lies in the complexity class UEOPL. We give an algorithm that finds an $\\varepsilon$-approximate fixed point of a three-dimensional monotone contraction using $O(\\log (1/\\varepsilon))$ queries to $f$. We also give a decomposition theorem that allows us to use this result to obtain an algorithm that finds an $\\varepsilon$-approximate fixed point of a $d$-dimensional monotone contraction usi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.10107","kind":"arxiv","version":2},"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/2411.10107/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"}