{"paper":{"title":"Computing Diverse and Nice Triangulations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Arturo Merino, Gibeom Park, Mayank Goswami, Meng-Tsung Tsai, Waldo G\\'alvez","submitted_at":"2025-06-02T05:10:16Z","abstract_excerpt":"We initiate the study of computing diverse triangulations to a given polygon. Given a simple $n$-gon $P$, an integer $ k \\geq 2 $, a quality measure $\\sigma$ on the set of triangulations of $P$ and a factor $ \\alpha \\geq 1 $, we formulate the Diverse and Nice Triangulations (DNT) problem that asks to compute $k$ \\emph{distinct} triangulations $T_1,\\dots,T_k$ of $P$ such that a) their diversity, $\\sum_{i < j} d(T_i,T_j) $, is as large as possible \\emph{and} b) they are nice, i.e., $\\sigma(T_i) \\leq \\alpha \\sigma^* $ for all $1\\leq i \\leq k$. Here, $d$ denotes the symmetric difference of edge se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01323","kind":"arxiv","version":3},"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/2506.01323/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"}