{"paper":{"title":"Efficient Encoding of Watermark Numbers as Reducible Permutation Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Maria Chroni, Stavros D. Nikolopoulos","submitted_at":"2011-10-06T09:24:51Z","abstract_excerpt":"In a software watermarking environment, several graph theoretic watermark methods use numbers as watermark values, where some of these methods encode the watermark numbers as graph structures. In this paper we extended the class of error correcting graphs by proposing an efficient and easily implemented codec system for encoding watermark numbers as reducible permutation flow-graphs. More precisely, we first present an efficient algorithm which encodes a watermark number $w$ as self-inverting permutation $\\pi^*$ and, then, an algorithm which encodes the self-inverting permutation $\\pi^*$ as a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1194","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":""},"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"}