{"paper":{"title":"Many-to-many Correspondences between Partitions: Introducing a Cut-based Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Henning Meyerhenke, Roland Glantz","submitted_at":"2016-03-15T18:01:13Z","abstract_excerpt":"Let $\\mathcal{P}$ and $\\mathcal{P}'$ be finite partitions of the set $V$. Finding good correspondences between the parts of $\\mathcal{P}$ and those of $\\mathcal{P}'$ is helpful in classification, pattern recognition, and network analysis. Unlike common similarity measures for partitions that yield only a single value, we provide specifics on how $\\mathcal{P}$ and $\\mathcal{P'}$ correspond to each other.\n  To this end, we first define natural collections of best correspondences under three constraints \\cone, \\ctwo, and \\cthree. In case of \\cone, the best correspondences form a minimum cut basis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04788","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":""},"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"}