{"paper":{"title":"On Randomized Memoryless Algorithms for the Weighted $k$-server Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ashish Chiplunkar, Sundar Vishwanathan","submitted_at":"2013-01-01T19:11:25Z","abstract_excerpt":"The weighted $k$-server problem is a generalization of the $k$-server problem in which the cost of moving a server of weight $\\beta_i$ through a distance $d$ is $\\beta_i\\cdot d$. The weighted server problem on uniform spaces models caching where caches have different write costs. We prove tight bounds on the performance of randomized memoryless algorithms for this problem on uniform metric spaces. We prove that there is an $\\alpha_k$-competitive memoryless algorithm for this problem, where $\\alpha_k=\\alpha_{k-1}^2+3\\alpha_{k-1}+1$; $\\alpha_1=1$. On the other hand we also prove that no randomiz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0123","kind":"arxiv","version":5},"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"}