{"paper":{"title":"Max-Distance Sparsification for Diversification and Clustering","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Soh Kumabe","submitted_at":"2024-11-05T06:34:29Z","abstract_excerpt":"Let $\\mathcal{D}$ be a set family that is the solution domain of some combinatorial problem. The \\emph{max-min diversification problem on $\\mathcal{D}$} is the problem to select $k$ sets from $\\mathcal{D}$ such that the Hamming distance between any two selected sets is at least $d$. FPT algorithms parameterized by $k+\\ell $, where $\\ell=\\max_{D\\in \\mathcal{D}}|D|$, and $k+d$ have been actively studied recently for several specific domains.\n  This paper provides unified algorithmic frameworks to solve this problem. Specifically, for each parameterization $k+\\ell $ and $k+d$, we provide an FPT o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.02845","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.02845/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"}