{"paper":{"title":"A Nearly-Linear Bound for Chasing Nested Convex Bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anupam Gupta, C.J. Argue, Michael B. Cohen, S\\'ebastien Bubeck, Yin Tat Lee","submitted_at":"2018-06-22T21:41:05Z","abstract_excerpt":"Friedman and Linial introduced the convex body chasing problem to explore the interplay between geometry and competitive ratio in metrical task systems. In convex body chasing, at each time step $t \\in \\mathbb{N}$, the online algorithm receives a request in the form of a convex body $K_t \\subseteq \\mathbb{R}^d$ and must output a point $x_t \\in K_t$. The goal is to minimize the total movement between consecutive output points, where the distance is measured in some given norm.\n  This problem is still far from being understood, and recently Bansal et al. gave an algorithm for the nested version,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08865","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"}