{"paper":{"title":"Stochastic Runtime Analysis of a Cross Entropy Algorithm for Traveling Salesman Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.NE"],"primary_cat":"cs.DS","authors_text":"Jianhui Lai, Rolf Moehring, Zijun Wu","submitted_at":"2016-12-21T03:24:26Z","abstract_excerpt":"This article analyzes the stochastic runtime of a Cross-Entropy Algorithm on two classes of traveling salesman problems. The algorithm shares main features of the famous Max-Min Ant System with iteration-best reinforcement.\n  For simple instances that have a $\\{1,n\\}$-valued distance function and a unique optimal solution, we prove a stochastic runtime of $O(n^{6+\\epsilon})$ with the vertex-based random solution generation, and a stochastic runtime of $O(n^{3+\\epsilon}\\ln n)$ with the edge-based random solution generation for an arbitrary $\\epsilon\\in (0,1)$. These runtimes are very close to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06962","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":""},"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"}