{"paper":{"title":"Greedy Vector Balancing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Arka Ghosh, Daniel Dadush, Ekin Ergen, {\\L}ukasz Orlikowski, S{\\l}awomir Lasota, Wojciech Czerwi\\'nski","submitted_at":"2026-06-16T14:42:12Z","abstract_excerpt":"In online vector balancing, vectors $t_1,\\dots,t_n$ arrive one by one from a given set $T$ and the goal is to assign signs $s_1,\\dots,s_n\\in\\{\\pm1\\}$ in an online manner so as to minimize the largest norm of any signed prefix sum $\\sum_{i=1}^ks_i t_i$, $k \\in [n]$. In this paper, we analyze the natural Euclidean greedy vector balancing algorithm for this problem: at each step $k$, the sign $s_k\\in\\{\\pm1\\}$ is chosen so that $s_k t_k$ has non-positive inner product with $\\sum_{i=1}^{k-1} s_i\\cdot t_i$. Our main result is the first finite bound, independent of the sequence length $n$, on the per"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17991","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17991/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"}