{"paper":{"title":"Random-Facet and Random-Bland require subexponential time even for shortest paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Oliver Friedmann, Thomas Dueholm Hansen, Uri Zwick","submitted_at":"2014-10-28T06:47:55Z","abstract_excerpt":"The Random-Facet algorithm of Kalai and of Matousek, Sharir and Welzl is an elegant randomized algorithm for solving linear programs and more general LP-type problems. Its expected subexponential time of $2^{\\tilde{O}(\\sqrt{m})}$, where $m$ is the number of inequalities, makes it the fastest known combinatorial algorithm for solving linear programs. We previously showed that Random-Facet performs an expected number of $2^{\\tilde{\\Omega}(\\sqrt[3]{m})}$ pivoting steps on some LPs with $m$ inequalities that correspond to $m$-action Markov Decision Processes (MDPs). We also showed that Random-Face"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7530","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"}