{"paper":{"title":"The Trie Measure, Revisited","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Bojana Kodric, Davide Cenzato, Jarno N. Alanko, Nicola Prezza, Ruben Becker, Sung-Hwan Kim, Travis Gagie","submitted_at":"2025-04-14T20:52:13Z","abstract_excerpt":"In this paper, we study the following problem: given $n$ subsets $S_1, \\dots, S_n$ of an integer universe $U = \\{0,\\dots, u-1\\}$, having total cardinality $N = \\sum_{i=1}^n |S_i|$, find a prefix-free encoding $enc : U \\rightarrow \\{0,1\\}^+$ minimizing the so-called trie measure, i.e., the total number of edges in the $n$ binary tries $\\mathcal T_1, \\dots, \\mathcal T_n$, where $\\mathcal T_i$ is the trie packing the encoded integers $\\{enc(x):x\\in S_i\\}$. We first observe that this problem is equivalent to that of merging $u$ sets with the cheapest sequence of binary unions, a problem which in ["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.10703","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/2504.10703/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"}