{"paper":{"title":"Optimal strategies for patrolling fences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.MA","math.CO"],"primary_cat":"cs.DS","authors_text":"Anders Martinsson, Bernhard Haeupler, Fabian Kuhn, Kalina Petrova, Pascal Pfister","submitted_at":"2018-09-18T13:45:14Z","abstract_excerpt":"A classical multi-agent fence patrolling problem asks: What is the maximum length $L$ of a line that $k$ agents with maximum speeds $v_1,\\ldots,v_k$ can patrol if each point on the line needs to be visited at least once every unit of time. It is easy to see that $L = \\alpha \\sum_{i=1}^k v_i$ for some efficiency $\\alpha \\in [\\frac{1}{2},1)$. After a series of works giving better and better efficiencies, it was conjectured that the best possible efficiency approaches $\\frac{2}{3}$. No upper bounds on the efficiency below $1$ were known. We prove the first such upper bounds and tightly bound the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06727","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"}