{"paper":{"title":"Online Vector Scheduling and Generalized Load Balancing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Guihai Chen, Qun Li, Weizhen Mao, Xiaojun Zhu","submitted_at":"2012-11-25T05:20:29Z","abstract_excerpt":"We give a polynomial time reduction from vector scheduling problem (VS) to generalized load balancing problem (GLB). This reduction gives the first non-trivial online algorithm for VS where vectors come in an online fashion. The online algorithm is very simple in that each vector only needs to minimize the $L_{\\ln(md)}$ norm of the resulting load when it comes, where $m$ is the number of partitions and $d$ is the dimension of vectors. It has an approximation bound of $e\\log(md)$, which is in $O(\\ln(md))$, so it also improves the $O(\\ln^2d)$ bound of the existing polynomial time algorithm for V"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5729","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"}