{"paper":{"title":"Diamonds are Forever in the Blockchain: Geometric Polyhedral Point-Set Pattern Matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"David M. Mount, Evrim Ozel, Gill Barequet, Martha C. Osegueda, Michael T. Goodrich, Shion Fukuzawa","submitted_at":"2022-08-11T00:32:54Z","abstract_excerpt":"Motivated by blockchain technology for supply-chain tracing of ethically sourced diamonds, we study geometric polyhedral point-set pattern matching as minimum-width polyhedral annulus problems under translations and rotations. We provide two $(1 + \\varepsilon)$-approximation schemes under translations with $O(\\varepsilon^{-d} n)$-time for $d$ dimensions and $O(n\\log \\varepsilon^{-1} + \\varepsilon^{-2})$-time for two dimensions, and we give an $O(f^{d-1}\\varepsilon^{1-2d}n)$-time algorithm when also allowing for rotations, parameterized on $f$, which we define as the slimness of the point set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05597","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/2208.05597/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"}