{"paper":{"title":"On Advice Complexity of the k-server Problem under Sparse Metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alejandro L\\'opez-Ortiz, Shahin Kamali, Sushmita Gupta","submitted_at":"2013-05-09T14:40:06Z","abstract_excerpt":"We consider the k-server problem under the advice model of computation when the underlying metric space is sparse. On one side, we show that an advice of size {\\Omega}(n) is required to obtain a 1-competitive algorithm for sequences of size n, even for the 2-server problem on a path metric of size N >= 5. Through another lower bound argument, we show that at least (n/2)(log {\\alpha} - 1.22) bits of advice is required to obtain an optimal solution for metric spaces of treewidth {\\alpha}, where 4 <= {\\alpha} < 2k. On the other side, we introduce {\\Theta}(1)-competitive algorithms for a wide rang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2108","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":""},"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"}