{"paper":{"title":"Optimal Dynamic Parameterized Subset Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DB"],"primary_cat":"cs.DS","authors_text":"Anthony Wirth, Hanzhi Wang, Junhao Gan, Seeun William Umboh, Zhuo Zhang","submitted_at":"2024-09-26T16:42:10Z","abstract_excerpt":"In this paper, we study the Dynamic Parameterized Subset Sampling (DPSS) problem in the Word RAM model. In DPSS, the input is a set,~$S$, of~$n$ items, where each item,~$x$, has a non-negative integer weight,~$w(x)$. Given a pair of query parameters, $(\\alpha, \\beta)$, each of which is a non-negative rational number, a parameterized subset sampling query on~$S$ seeks to return a subset $T \\subseteq S$ such that each item $x \\in S$ is selected in~$T$, independently, with probability $p_x(\\alpha, \\beta) = \\min \\left\\{\\frac{w(x)}{\\alpha \\sum_{x\\in S} w(x)+\\beta}, 1 \\right\\}$. More specifically, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.18036","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/2409.18036/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"}